detailed information: The input equation set is:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| | 32 | A | + | | 16 | B | + | | 8 | C | + | | 4 | D | + | | 2 | E | + | | F | = | | 1 | | (2) |
| | 243 | A | + | | 81 | B | + | | 27 | C | + | | 9 | D | + | | 3 | E | + | | F | = | | 4 | | (3) |
| | 1024 | A | + | | 256 | B | + | | 64 | C | + | | 16 | D | + | | 4 | E | + | | F | = | | 5 | | (4) |
| | 3125 | A | + | | 625 | B | + | | 125 | C | + | | 25 | D | + | | 5 | E | + | | F | = | | 1 | | (5) |
| | 7776 | A | + | | 1296 | B | + | | 216 | C | + | | 36 | D | + | | 6 | E | + | | F | = | | 4 | | (6) |
| Question solving process:
Multiply both sides of equation (1) by 32, the equation can be obtained: | | 32 | A | + | | 32 | B | + | | 32 | C | + | | 32 | D | + | | 32 | E | + | | 32 | F | = | | 32 | (7) | , then subtract both sides of equation (7) from both sides of equation (2), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | | -31 | F | = | | -31 | | (2) |
| | 243 | A | + | | 81 | B | + | | 27 | C | + | | 9 | D | + | | 3 | E | + | | F | = | | 4 | | (3) |
| | 1024 | A | + | | 256 | B | + | | 64 | C | + | | 16 | D | + | | 4 | E | + | | F | = | | 5 | | (4) |
| | 3125 | A | + | | 625 | B | + | | 125 | C | + | | 25 | D | + | | 5 | E | + | | F | = | | 1 | | (5) |
| | 7776 | A | + | | 1296 | B | + | | 216 | C | + | | 36 | D | + | | 6 | E | + | | F | = | | 4 | | (6) |
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Multiply both sides of equation (1) by 243, the equation can be obtained: | | 243 | A | + | | 243 | B | + | | 243 | C | + | | 243 | D | + | | 243 | E | + | | 243 | F | = | | 243 | (8) | , then subtract both sides of equation (8) from both sides of equation (3), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | | -31 | F | = | | -31 | | (2) |
| -162 | B | | -216 | C | | -234 | D | | -240 | E | | -242 | F | = | | -239 | | (3) |
| | 1024 | A | + | | 256 | B | + | | 64 | C | + | | 16 | D | + | | 4 | E | + | | F | = | | 5 | | (4) |
| | 3125 | A | + | | 625 | B | + | | 125 | C | + | | 25 | D | + | | 5 | E | + | | F | = | | 1 | | (5) |
| | 7776 | A | + | | 1296 | B | + | | 216 | C | + | | 36 | D | + | | 6 | E | + | | F | = | | 4 | | (6) |
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Multiply both sides of equation (1) by 1024, the equation can be obtained: | | 1024 | A | + | | 1024 | B | + | | 1024 | C | + | | 1024 | D | + | | 1024 | E | + | | 1024 | F | = | | 1024 | (9) | , then subtract both sides of equation (9) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | | -31 | F | = | | -31 | | (2) |
| -162 | B | | -216 | C | | -234 | D | | -240 | E | | -242 | F | = | | -239 | | (3) |
| -768 | B | | -960 | C | | -1008 | D | | -1020 | E | | -1023 | F | = | | -1019 | | (4) |
| | 3125 | A | + | | 625 | B | + | | 125 | C | + | | 25 | D | + | | 5 | E | + | | F | = | | 1 | | (5) |
| | 7776 | A | + | | 1296 | B | + | | 216 | C | + | | 36 | D | + | | 6 | E | + | | F | = | | 4 | | (6) |
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Multiply both sides of equation (1) by 3125, the equation can be obtained: | | 3125 | A | + | | 3125 | B | + | | 3125 | C | + | | 3125 | D | + | | 3125 | E | + | | 3125 | F | = | | 3125 | (10) | , then subtract both sides of equation (10) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | | -31 | F | = | | -31 | | (2) |
| -162 | B | | -216 | C | | -234 | D | | -240 | E | | -242 | F | = | | -239 | | (3) |
| -768 | B | | -960 | C | | -1008 | D | | -1020 | E | | -1023 | F | = | | -1019 | | (4) |
| -2500 | B | | -3000 | C | | -3100 | D | | -3120 | E | | -3124 | F | = | | -3124 | | (5) |
| | 7776 | A | + | | 1296 | B | + | | 216 | C | + | | 36 | D | + | | 6 | E | + | | F | = | | 4 | | (6) |
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Multiply both sides of equation (1) by 7776, the equation can be obtained: | | 7776 | A | + | | 7776 | B | + | | 7776 | C | + | | 7776 | D | + | | 7776 | E | + | | 7776 | F | = | | 7776 | (11) | , then subtract both sides of equation (11) from both sides of equation (6), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | | -31 | F | = | | -31 | | (2) |
| -162 | B | | -216 | C | | -234 | D | | -240 | E | | -242 | F | = | | -239 | | (3) |
| -768 | B | | -960 | C | | -1008 | D | | -1020 | E | | -1023 | F | = | | -1019 | | (4) |
| -2500 | B | | -3000 | C | | -3100 | D | | -3120 | E | | -3124 | F | = | | -3124 | | (5) |
| -6480 | B | | -7560 | C | | -7740 | D | | -7770 | E | | -7775 | F | = | | -7772 | | (6) |
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Multiply both sides of equation (2) by 81 Divide the two sides of equation (2) by 8, the equation can be obtained: | -162 | B | | -243 | C | | - | 567 2 | D | | - | 1215 4 | E | | - | 2511 8 | F | = | | - | 2511 8 | (12) | , then subtract both sides of equation (12) from both sides of equation (3), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | | -31 | F | = | | -31 | | (2) |
| | 27 | C | + | | | 99 2 | D | + | | | 255 4 | E | + | | | 575 8 | F | = | | | 599 8 | | (3) |
| -768 | B | | -960 | C | | -1008 | D | | -1020 | E | | -1023 | F | = | | -1019 | | (4) |
| -2500 | B | | -3000 | C | | -3100 | D | | -3120 | E | | -3124 | F | = | | -3124 | | (5) |
| -6480 | B | | -7560 | C | | -7740 | D | | -7770 | E | | -7775 | F | = | | -7772 | | (6) |
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Multiply both sides of equation (2) by 48, the equation can be obtained: | -768 | B | | -1152 | C | | -1344 | D | | -1440 | E | | -1488 | F | = | | -1488 | (13) | , then subtract both sides of equation (13) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | | -31 | F | = | | -31 | | (2) |
| | 27 | C | + | | | 99 2 | D | + | | | 255 4 | E | + | | | 575 8 | F | = | | | 599 8 | | (3) |
| | 192 | C | + | | 336 | D | + | | 420 | E | + | | 465 | F | = | | 469 | | (4) |
| -2500 | B | | -3000 | C | | -3100 | D | | -3120 | E | | -3124 | F | = | | -3124 | | (5) |
| -6480 | B | | -7560 | C | | -7740 | D | | -7770 | E | | -7775 | F | = | | -7772 | | (6) |
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Multiply both sides of equation (2) by 625 Divide the two sides of equation (2) by 4, the equation can be obtained: | -2500 | B | | -3750 | C | | -4375 | D | | - | 9375 2 | E | | - | 19375 4 | F | = | | - | 19375 4 | (14) | , then subtract both sides of equation (14) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | | -31 | F | = | | -31 | | (2) |
| | 27 | C | + | | | 99 2 | D | + | | | 255 4 | E | + | | | 575 8 | F | = | | | 599 8 | | (3) |
| | 192 | C | + | | 336 | D | + | | 420 | E | + | | 465 | F | = | | 469 | | (4) |
| | 750 | C | + | | 1275 | D | + | | | 3135 2 | E | + | | | 6879 4 | F | = | | | 6879 4 | | (5) |
| -6480 | B | | -7560 | C | | -7740 | D | | -7770 | E | | -7775 | F | = | | -7772 | | (6) |
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Multiply both sides of equation (2) by 405, the equation can be obtained: | -6480 | B | | -9720 | C | | -11340 | D | | -12150 | E | | -12555 | F | = | | -12555 | (15) | , then subtract both sides of equation (15) from both sides of equation (6), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | | -31 | F | = | | -31 | | (2) |
| | 27 | C | + | | | 99 2 | D | + | | | 255 4 | E | + | | | 575 8 | F | = | | | 599 8 | | (3) |
| | 192 | C | + | | 336 | D | + | | 420 | E | + | | 465 | F | = | | 469 | | (4) |
| | 750 | C | + | | 1275 | D | + | | | 3135 2 | E | + | | | 6879 4 | F | = | | | 6879 4 | | (5) |
| | 2160 | C | + | | 3600 | D | + | | 4380 | E | + | | 4780 | F | = | | 4783 | | (6) |
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Multiply both sides of equation (3) by 64 Divide the two sides of equation (3) by 9, the equation can be obtained: | | 192 | C | + | | 352 | D | + | | | 1360 3 | E | + | | | 4600 9 | F | = | | | 4792 9 | (16) | , then subtract both sides of equation (16) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | | -31 | F | = | | -31 | | (2) |
| | 27 | C | + | | | 99 2 | D | + | | | 255 4 | E | + | | | 575 8 | F | = | | | 599 8 | | (3) |
| -16 | D | | - | 100 3 | E | | - | 415 9 | F | = | | - | 571 9 | | (4) |
| | 750 | C | + | | 1275 | D | + | | | 3135 2 | E | + | | | 6879 4 | F | = | | | 6879 4 | | (5) |
| | 2160 | C | + | | 3600 | D | + | | 4380 | E | + | | 4780 | F | = | | 4783 | | (6) |
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Multiply both sides of equation (3) by 250 Divide the two sides of equation (3) by 9, the equation can be obtained: | | 750 | C | + | | 1375 | D | + | | | 10625 6 | E | + | | | 71875 36 | F | = | | | 74875 36 | (17) | , then subtract both sides of equation (17) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | | -31 | F | = | | -31 | | (2) |
| | 27 | C | + | | | 99 2 | D | + | | | 255 4 | E | + | | | 575 8 | F | = | | | 599 8 | | (3) |
| -16 | D | | - | 100 3 | E | | - | 415 9 | F | = | | - | 571 9 | | (4) |
| -100 | D | | - | 610 3 | E | | - | 2491 9 | F | = | | - | 3241 9 | | (5) |
| | 2160 | C | + | | 3600 | D | + | | 4380 | E | + | | 4780 | F | = | | 4783 | | (6) |
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Multiply both sides of equation (3) by 80, the equation can be obtained: | | 2160 | C | + | | 3960 | D | + | | 5100 | E | + | | 5750 | F | = | | 5990 | (18) | , then subtract both sides of equation (18) from both sides of equation (6), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | | -31 | F | = | | -31 | | (2) |
| | 27 | C | + | | | 99 2 | D | + | | | 255 4 | E | + | | | 575 8 | F | = | | | 599 8 | | (3) |
| -16 | D | | - | 100 3 | E | | - | 415 9 | F | = | | - | 571 9 | | (4) |
| -100 | D | | - | 610 3 | E | | - | 2491 9 | F | = | | - | 3241 9 | | (5) |
| -360 | D | | -720 | E | | -970 | F | = | | -1207 | | (6) |
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Multiply both sides of equation (4) by 25 Divide the two sides of equation (4) by 4, the equation can be obtained: | -100 | D | | - | 625 3 | E | | - | 10375 36 | F | = | | - | 14275 36 | (19) | , then subtract both sides of equation (19) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | | -31 | F | = | | -31 | | (2) |
| | 27 | C | + | | | 99 2 | D | + | | | 255 4 | E | + | | | 575 8 | F | = | | | 599 8 | | (3) |
| -16 | D | | - | 100 3 | E | | - | 415 9 | F | = | | - | 571 9 | | (4) |
| | -360 | D | | -720 | E | | -970 | F | = | | -1207 | | (6) |
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Multiply both sides of equation (4) by 45 Divide the two sides of equation (4) by 2, the equation can be obtained: | -360 | D | | -750 | E | | - | 2075 2 | F | = | | - | 2855 2 | (20) | , then subtract both sides of equation (20) from both sides of equation (6), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | | -31 | F | = | | -31 | | (2) |
| | 27 | C | + | | | 99 2 | D | + | | | 255 4 | E | + | | | 575 8 | F | = | | | 599 8 | | (3) |
| -16 | D | | - | 100 3 | E | | - | 415 9 | F | = | | - | 571 9 | | (4) |
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Multiply both sides of equation (5) by 6, the equation can be obtained: , then subtract both sides of equation (21) from both sides of equation (6), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | | -31 | F | = | | -31 | | (2) |
| | 27 | C | + | | | 99 2 | D | + | | | 255 4 | E | + | | | 575 8 | F | = | | | 599 8 | | (3) |
| -16 | D | | - | 100 3 | E | | - | 415 9 | F | = | | - | 571 9 | | (4) |
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Multiply both sides of equation (6) by 137 Divide both sides of equation (6) by 12, get the equation:, then add the two sides of equation (22) to both sides of equation (5), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | | -31 | F | = | | -31 | | (2) |
| | 27 | C | + | | | 99 2 | D | + | | | 255 4 | E | + | | | 575 8 | F | = | | | 599 8 | | (3) |
| -16 | D | | - | 100 3 | E | | - | 415 9 | F | = | | - | 571 9 | | (4) |
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Multiply both sides of equation (6) by 415 Divide both sides of equation (6) by 9, get the equation:, then subtract both sides of equation (23) from both sides of equation (4), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | | -31 | F | = | | -31 | | (2) |
| | 27 | C | + | | | 99 2 | D | + | | | 255 4 | E | + | | | 575 8 | F | = | | | 599 8 | | (3) |
| -16 | D | | - | 100 3 | E | = | | - | 467 3 | | (4) |
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Multiply both sides of equation (6) by 575 Divide both sides of equation (6) by 8, get the equation:, then add the two sides of equation (24) to both sides of equation (3), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | | -31 | F | = | | -31 | | (2) |
| | 27 | C | + | | | 99 2 | D | + | | | 255 4 | E | = | | | 1749 8 | | (3) |
| -16 | D | | - | 100 3 | E | = | | - | 467 3 | | (4) |
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Multiply both sides of equation (6) by 31, get the equation:, then subtract both sides of equation (25) from both sides of equation (2), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | + | | F | = | | 1 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | = | | -93 | | (2) |
| | 27 | C | + | | | 99 2 | D | + | | | 255 4 | E | = | | | 1749 8 | | (3) |
| -16 | D | | - | 100 3 | E | = | | - | 467 3 | | (4) |
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Add both sides of equation (6) to both sides of equation (1), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 3 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | = | | -93 | | (2) |
| | 27 | C | + | | | 99 2 | D | + | | | 255 4 | E | = | | | 1749 8 | | (3) |
| -16 | D | | - | 100 3 | E | = | | - | 467 3 | | (4) |
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Multiply both sides of equation (5) by 20 Divide both sides of equation (5) by 3, get the equation:, then add the two sides of equation (26) to both sides of equation (4), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 3 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | = | | -93 | | (2) |
| | 27 | C | + | | | 99 2 | D | + | | | 255 4 | E | = | | | 1749 8 | | (3) |
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Multiply both sides of equation (5) by 51 Divide both sides of equation (5) by 4, get the equation:, then subtract both sides of equation (27) from both sides of equation (3), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 3 | | (1) |
| -16 | B | | -24 | C | | -28 | D | | -30 | E | = | | -93 | | (2) |
| | 27 | C | + | | | 99 2 | D | = | | - | 8589 16 | | (3) |
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Multiply both sides of equation (5) by 6, get the equation:, then add the two sides of equation (28) to both sides of equation (2), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 3 | | (1) |
| -16 | B | | -24 | C | | -28 | D | = | | | 525 2 | | (2) |
| | 27 | C | + | | | 99 2 | D | = | | - | 8589 16 | | (3) |
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Divide both sides of equation (5) by 5, get the equation:, then subtract both sides of equation (29) from both sides of equation (1), get the equation:
| | | | A | + | | B | + | | C | + | | D | = | | - | 177 20 | | (1) |
| -16 | B | | -24 | C | | -28 | D | = | | | 525 2 | | (2) |
| | 27 | C | + | | | 99 2 | D | = | | - | 8589 16 | | (3) |
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Multiply both sides of equation (4) by 99 Divide both sides of equation (4) by 32, get the equation:, then add the two sides of equation (30) to both sides of equation (3), get the equation:
| | | | A | + | | B | + | | C | + | | D | = | | - | 177 20 | | (1) |
| -16 | B | | -24 | C | | -28 | D | = | | | 525 2 | | (2) |
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Multiply both sides of equation (4) by 7 Divide both sides of equation (4) by 4, get the equation:, then subtract both sides of equation (31) from both sides of equation (2), get the equation:
| | | | A | + | | B | + | | C | + | | D | = | | - | 177 20 | | (1) |
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Divide both sides of equation (4) by 16, get the equation:, then add the two sides of equation (32) to both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 8 Divide both sides of equation (3) by 9, get the equation:, then add the two sides of equation (33) to both sides of equation (2), get the equation:
Divide both sides of equation (3) by 27, get the equation:, then subtract both sides of equation (34) from both sides of equation (1), get the equation:
Divide both sides of equation (2) by 16, get the equation:, then add the two sides of equation (35) to both sides of equation (1), get the equation:
The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
Therefore, the solution of the equation set is:
Convert the solution of the equation set to decimals:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |