detailed information: The input equation set is:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| | 16 | A | + | | 8 | B | + | | 4 | C | + | | 2 | D | + | | E | = | | -29 | | (2) |
| | 81 | A | + | | 27 | B | + | | 9 | C | + | | 3 | D | + | | E | = | | -237 | | (3) |
| | 256 | A | + | | 64 | B | + | | 16 | C | + | | 4 | D | + | | E | = | | -1014 | | (4) |
| | 625 | A | + | | 125 | B | + | | 25 | C | + | | 5 | D | + | | E | = | | -3110 | | (5) |
| Question solving process:
Multiply both sides of equation (1) by 16, the equation can be obtained: | | 16 | A | + | | 16 | B | + | | 16 | C | + | | 16 | D | + | | 16 | E | = | | 0 | (6) | , then subtract both sides of equation (6) from both sides of equation (2), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -29 | | (2) |
| | 81 | A | + | | 27 | B | + | | 9 | C | + | | 3 | D | + | | E | = | | -237 | | (3) |
| | 256 | A | + | | 64 | B | + | | 16 | C | + | | 4 | D | + | | E | = | | -1014 | | (4) |
| | 625 | A | + | | 125 | B | + | | 25 | C | + | | 5 | D | + | | E | = | | -3110 | | (5) |
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Multiply both sides of equation (1) by 81, the equation can be obtained: | | 81 | A | + | | 81 | B | + | | 81 | C | + | | 81 | D | + | | 81 | E | = | | 0 | (7) | , then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -29 | | (2) |
| -54 | B | | -72 | C | | -78 | D | | -80 | E | = | | -237 | | (3) |
| | 256 | A | + | | 64 | B | + | | 16 | C | + | | 4 | D | + | | E | = | | -1014 | | (4) |
| | 625 | A | + | | 125 | B | + | | 25 | C | + | | 5 | D | + | | E | = | | -3110 | | (5) |
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Multiply both sides of equation (1) by 256, the equation can be obtained: | | 256 | A | + | | 256 | B | + | | 256 | C | + | | 256 | D | + | | 256 | E | = | | 0 | (8) | , then subtract both sides of equation (8) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -29 | | (2) |
| -54 | B | | -72 | C | | -78 | D | | -80 | E | = | | -237 | | (3) |
| -192 | B | | -240 | C | | -252 | D | | -255 | E | = | | -1014 | | (4) |
| | 625 | A | + | | 125 | B | + | | 25 | C | + | | 5 | D | + | | E | = | | -3110 | | (5) |
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Multiply both sides of equation (1) by 625, the equation can be obtained: | | 625 | A | + | | 625 | B | + | | 625 | C | + | | 625 | D | + | | 625 | E | = | | 0 | (9) | , then subtract both sides of equation (9) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -29 | | (2) |
| -54 | B | | -72 | C | | -78 | D | | -80 | E | = | | -237 | | (3) |
| -192 | B | | -240 | C | | -252 | D | | -255 | E | = | | -1014 | | (4) |
| -500 | B | | -600 | C | | -620 | D | | -624 | E | = | | -3110 | | (5) |
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Multiply both sides of equation (2) by 27 Divide the two sides of equation (2) by 4, the equation can be obtained: | -54 | B | | -81 | C | | - | 189 2 | D | | - | 405 4 | E | = | | - | 783 4 | (10) | , then subtract both sides of equation (10) from both sides of equation (3), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -29 | | (2) |
| | 9 | C | + | | | 33 2 | D | + | | | 85 4 | E | = | | - | 165 4 | | (3) |
| -192 | B | | -240 | C | | -252 | D | | -255 | E | = | | -1014 | | (4) |
| -500 | B | | -600 | C | | -620 | D | | -624 | E | = | | -3110 | | (5) |
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Multiply both sides of equation (2) by 24, the equation can be obtained: | -192 | B | | -288 | C | | -336 | D | | -360 | E | = | | -696 | (11) | , then subtract both sides of equation (11) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -29 | | (2) |
| | 9 | C | + | | | 33 2 | D | + | | | 85 4 | E | = | | - | 165 4 | | (3) |
| | 48 | C | + | | 84 | D | + | | 105 | E | = | | -318 | | (4) |
| -500 | B | | -600 | C | | -620 | D | | -624 | E | = | | -3110 | | (5) |
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Multiply both sides of equation (2) by 125 Divide the two sides of equation (2) by 2, the equation can be obtained: | -500 | B | | -750 | C | | -875 | D | | - | 1875 2 | E | = | | - | 3625 2 | (12) | , then subtract both sides of equation (12) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -29 | | (2) |
| | 9 | C | + | | | 33 2 | D | + | | | 85 4 | E | = | | - | 165 4 | | (3) |
| | 48 | C | + | | 84 | D | + | | 105 | E | = | | -318 | | (4) |
| | 150 | C | + | | 255 | D | + | | | 627 2 | E | = | | - | 2595 2 | | (5) |
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Multiply both sides of equation (3) by 16 Divide the two sides of equation (3) by 3, the equation can be obtained: | | 48 | C | + | | 88 | D | + | | | 340 3 | E | = | | -220 | (13) | , then subtract both sides of equation (13) from both sides of equation (4), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -29 | | (2) |
| | 9 | C | + | | | 33 2 | D | + | | | 85 4 | E | = | | - | 165 4 | | (3) |
| | | 150 | C | + | | 255 | D | + | | | 627 2 | E | = | | - | 2595 2 | | (5) |
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Multiply both sides of equation (3) by 50 Divide the two sides of equation (3) by 3, the equation can be obtained: | | 150 | C | + | | 275 | D | + | | | 2125 6 | E | = | | - | 1375 2 | (14) | , then subtract both sides of equation (14) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -29 | | (2) |
| | 9 | C | + | | | 33 2 | D | + | | | 85 4 | E | = | | - | 165 4 | | (3) |
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Multiply both sides of equation (4) by 5, the equation can be obtained: , then subtract both sides of equation (15) from both sides of equation (5), the equations are reduced to:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -29 | | (2) |
| | 9 | C | + | | | 33 2 | D | + | | | 85 4 | E | = | | - | 165 4 | | (3) |
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Multiply both sides of equation (5) by 25 Divide both sides of equation (5) by 3, get the equation:, then add the two sides of equation (16) to both sides of equation (4), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -29 | | (2) |
| | 9 | C | + | | | 33 2 | D | + | | | 85 4 | E | = | | - | 165 4 | | (3) |
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Multiply both sides of equation (5) by 85 Divide both sides of equation (5) by 4, get the equation:, then subtract both sides of equation (17) from both sides of equation (3), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| -8 | B | | -12 | C | | -14 | D | | -15 | E | = | | -29 | | (2) |
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Multiply both sides of equation (5) by 15, get the equation:, then add the two sides of equation (18) to both sides of equation (2), get the equation:
| | | | A | + | | B | + | | C | + | | D | + | | E | = | | 0 | | (1) |
| -8 | B | | -12 | C | | -14 | D | = | | -1829 | | (2) |
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Subtract both sides of equation (5) from both sides of equation (1), get the equation:
| | | | -8 | B | | -12 | C | | -14 | D | = | | -1829 | | (2) |
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Multiply both sides of equation (4) by 33 Divide both sides of equation (4) by 8, get the equation:, then add the two sides of equation (19) to both sides of equation (3), get the equation:
| | | | -8 | B | | -12 | C | | -14 | D | = | | -1829 | | (2) |
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Multiply both sides of equation (4) by 7 Divide both sides of equation (4) by 2, get the equation:, then subtract both sides of equation (20) from both sides of equation (2), get the equation:
Divide both sides of equation (4) by 4, get the equation:, then add the two sides of equation (21) to both sides of equation (1), get the equation:
Multiply both sides of equation (3) by 4 Divide both sides of equation (3) by 3, get the equation:, then add the two sides of equation (22) to both sides of equation (2), get the equation:
Divide both sides of equation (3) by 9, get the equation:, then subtract both sides of equation (23) from both sides of equation (1), get the equation:
Divide both sides of equation (2) by 8, get the equation:, then add the two sides of equation (24) 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》 |