总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 [(15+12)x(35-x)+(11+12)x]x2+[15x(35-x)+11x]x6 = 4400 的解.
题型:方程
解:原方程: | ( | ( | 15 | + | 12 | ) | x | ( | 35 | − | x | ) | + | ( | 11 | + | 12 | ) | x | ) | x | × | 2 | + | ( | 15 | x | ( | 35 | − | x | ) | + | 11 | x | ) | x | × | 6 | = | 4400 |
去掉方程左边的括号:
方程左边 = | ( | 15 | + | 12 | ) | x | ( | 35 | − | x | ) | x | × | 2 | + | ( | 11 | + | 12 | ) | x | x | × | 2 | + | ( | 15 | x | ( | 35 | − | x | ) | + | 11 | x | ) | x | × | 6 |
= | 15 | x | ( | 35 | − | x | ) | x | × | 2 | + | 12 | x | ( | 35 | − | x | ) | x | × | 2 | + | ( | 11 | + | 12 | ) | x |
= | 30 | x | ( | 35 | − | x | ) | x | + | 24 | x | ( | 35 | − | x | ) | x | + | ( | 11 | + | 12 | ) | x | x | × | 2 |
= | 30 | x | × | 35 | x | − | 30 | x | x | x | + | 24 | x | ( | 35 | − | x | ) | x |
= | 1050 | x | x | − | 30 | x | x | x | + | 24 | x | ( | 35 | − | x | ) | x | + | ( | 11 | + | 12 | ) |
= | 1050 | x | x | − | 30 | x | x | x | + | 24 | x | × | 35 | x | − | 24 |
= | 1050 | x | x | − | 30 | x | x | x | + | 840 | x | x | − | 24 | x |
= | 1050 | x | x | − | 30 | x | x | x | + | 840 | x | x | − | 24 | x |
= | 1050 | x | x | − | 30 | x | x | x | + | 840 | x | x | − | 24 | x |
= | 1050 | x | x | − | 30 | x | x | x | + | 840 | x | x | − | 24 | x |
= | 1050 | x | x | − | 30 | x | x | x | + | 840 | x | x | − | 24 | x |
= | 1050 | x | x | − | 30 | x | x | x | + | 840 | x | x | − | 24 | x |
= | 1050 | x | x | − | 30 | x | x | x | + | 840 | x | x | − | 24 | x |
方程化为:
| 1050 | x | x | − | 30 | x | x | x | + | 840 | x | x | − | 24 | x | = | 4400 |
方程的解为:
x1≈-0.912576 ,保留6位小数
x2≈0.936479 ,保留6位小数
x3≈35.753875 ,保留6位小数
有 3个解。
解程的详细方法请参阅:《方程的解法》
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