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    总述:本次共解1题。其中
           ☆方程1题

〖 1/1方程〗
    作业:求方程 2.22 = ((25.53*0.591(x+0.1))/(1+0.591(x+0.1))*((100-19.9-0.96)/100)*(1/(1+0.31*0.96)+((3.47(x+0.1))/(1.39*0.101325)) ) ) 的解.
    题型:方程
    解:原方程:
     
111
50
= ((
2553
100
×
591
1000
( x +
1
10
)) ÷ (1 +
591
1000
( x +
1
10
)) × ((100 −
199
10
−
24
25
) ÷ 100)(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
))))
    去掉方程右边的一个括号:
     
111
50
= (
2553
100
×
591
1000
( x +
1
10
)) ÷ (1 +
591
1000
( x +
1
10
)) × ((100 −
199
10
−
24
25
) ÷ 100)(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)))
     方程两边同时乘以:(1 +
591
1000
( x +
1
10
))
     
111
50
(1 +
591
1000
( x +
1
10
)) = (
2553
100
×
591
1000
( x +
1
10
))((100 −
199
10
−
24
25
) ÷ 100)(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)))
    去掉方程左边的一个括号:
     
111
50
× 1 +
111
50
×
591
1000
( x +
1
10
) = (
2553
100
×
591
1000
( x +
1
10
))((100 −
199
10
−
24
25
) ÷ 100)(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)))
    去掉方程右边的一个括号:
     
111
50
× 1 +
111
50
×
591
1000
( x +
1
10
) =
2553
100
×
591
1000
( x +
1
10
)((100 −
199
10
−
24
25
) ÷ 100)(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)))
    方程化简为:
     
111
50
+
65601
50000
( x +
1
10
) =
1508823
100000
( x +
1
10
)((100 −
199
10
−
24
25
) ÷ 100)(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)))
    去掉方程左边的一个括号:
     
111
50
+
65601
50000
x +
65601
50000
×
1
10
=
1508823
100000
( x +
1
10
)((100 −
199
10
−
24
25
) ÷ 100)(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)))
    去掉方程右边的一个括号:
     
111
50
+
65601
50000
x +
65601
50000
×
1
10
=
1508823
100000
x ((100 −
199
10
−
24
25
) ÷ 100)(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
))) +
1508823
100000
×
1
10
((100 −
199
10
−
24
25
) ÷ 100)(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)))
    方程化简为:
     
111
50
+
65601
50000
x +
65601
500000
=
1508823
100000
x ((100 −
199
10
−
24
25
) ÷ 100)(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
))) +
1508823
1000000
((100 −
199
10
−
24
25
) ÷ 100)(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)))
    方程化简为:
     
1175601
500000
+
65601
50000
x =
1508823
100000
x ((100 −
199
10
−
24
25
) ÷ 100)(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
))) +
1508823
1000000
((100 −
199
10
−
24
25
) ÷ 100)(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)))
    去掉方程右边的一个括号:
     
1175601
500000
+
65601
50000
x =
1508823
100000
x (100 −
199
10
−
24
25
) ÷ 100 × (1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
))) +
1508823
1000000
((100 −
199
10
−
24
25
) ÷ 100)(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)))
    方程化简为:
     
1175601
500000
+
65601
50000
x =
1508823
10000000
x (100 −
199
10
−
24
25
)(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
))) +
1508823
1000000
((100 −
199
10
−
24
25
) ÷ 100)(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)))
    去掉方程右边的一个括号:
     
1175601
500000
+
65601
50000
x =
1508823
10000000
x × 100(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
))) −
1508823
10000000
x ×
199
10
(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
))) −
1508823
10000000
x ×
24
25
(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)))
    方程化简为:
     
1175601
500000
+
65601
50000
x =
1508823
100000
x (1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
))) −
300255777
100000000
x (1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
))) −
4526469
31250000
x (1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
))) +
1508823
1000000
((100 −
199
10
−
24
25
) ÷ 100)(1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)))
    去掉方程右边的一个括号:
     
1175601
500000
+
65601
50000
x =
1508823
100000
x × 1 ÷ (1 +
31
100
×
24
25
) +
1508823
100000
x ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)) −
300255777
100000000
x (1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
))) −
4526469
31250000
x
    方程化简为:
     
1175601
500000
+
65601
50000
x =
1508823
100000
x ÷ (1 +
31
100
×
24
25
) +
1508823
100000
x ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)) −
300255777
100000000
x (1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
))) −
4526469
31250000
x (1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)))
     方程两边同时乘以:(1 +
31
100
×
24
25
)
     
1175601
500000
(1 +
31
100
×
24
25
) +
65601
50000
x (1 +
31
100
×
24
25
) =
1508823
100000
x +
1508823
100000
x ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
))(1 +
31
100
×
24
25
) −
300255777
100000000
x (1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)))(1 +
31
100
×
24
25
) −
4526469
31250000
x
    去掉方程左边的一个括号:
     
1175601
500000
× 1 +
1175601
500000
×
31
100
×
24
25
+
65601
50000
x (1 +
31
100
×
24
25
) =
1508823
100000
x +
1508823
100000
x ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
))(1 +
31
100
×
24
25
) −
300255777
100000000
x (1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)))(1 +
31
100
×
24
25
) −
4526469
31250000
x
    去掉方程右边的一个括号:
     
1175601
500000
× 1 +
1175601
500000
×
31
100
×
24
25
+
65601
50000
x (1 +
31
100
×
24
25
) =
1508823
100000
x +
1508823
100000
x (
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
) × (1 +
31
100
×
24
25
) −
300255777
100000000
x (1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)))(1 +
31
100
×
24
25
) −
4526469
31250000
    方程化简为:
     
1175601
500000
+
109330893
156250000
+
65601
50000
x (1 +
31
100
×
24
25
) =
1508823
100000
x +
1508823
100000
x (
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
) × (1 +
31
100
×
24
25
) −
300255777
100000000
x (1 ÷ (1 +
31
100
×
24
25
) + ((
347
100
( x +
1
10
)) ÷ (
139
100
×
4053
40000
)))(1 +
31
100
×
24
25
) −
4526469
31250000


    方程的解为:
        x1≈-1.792047 ,保留6位小数
        x2≈0.181361 ,保留6位小数
    
    有 2个解。


解程的详细方法请参阅:《方程的解法》



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