总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 85000/(288000x/(288000+x)+17000) = 5(16x/(16+x)+120)/(16x/(16+x)+120+x) 的解.
题型:方程
解:原方程:| | 85000 | ÷ | ( | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 17000 | ) | = | 5 | ( | 16 | x | ÷ | ( | 16 | + | x | ) | + | 120 | ) | ÷ | ( | 16 | x | ÷ | ( | 16 | + | x | ) | + | 120 | + | x | ) |
| 方程两边同时乘以: | ( | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 17000 | ) | , | ( | 16 | x | ÷ | ( | 16 | + | x | ) | + | 120 | + | x | ) |
| | 85000 | ( | 16 | x | ÷ | ( | 16 | + | x | ) | + | 120 | + | x | ) | = | 5 | ( | 16 | x | ÷ | ( | 16 | + | x | ) | + | 120 | ) | ( | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 17000 | ) |
去掉方程左边的一个括号:
| | 85000 | × | 16 | x | ÷ | ( | 16 | + | x | ) | + | 85000 | × | 120 | + | 85000 | x | = | 5 | ( | 16 | x | ÷ | ( | 16 | + | x | ) | + | 120 | ) | ( | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 17000 | ) |
去掉方程右边的一个括号:
| | 85000 | × | 16 | x | ÷ | ( | 16 | + | x | ) | + | 85000 | × | 120 | + | 85000 | x | = | 5 | × | 16 | x | ÷ | ( | 16 | + | x | ) | × | ( | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 17000 | ) | + | 5 | × | 120 | ( | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 17000 | ) |
方程化简为:
| | 1360000 | x | ÷ | ( | 16 | + | x | ) | + | 10200000 | + | 85000 | x | = | 80 | x | ÷ | ( | 16 | + | x | ) | × | ( | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 17000 | ) | + | 600 | ( | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 17000 | ) |
| | 1360000 | x | + | 10200000 | ( | 16 | + | x | ) | + | 85000 | x | ( | 16 | + | x | ) | = | 80 | x | ( | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 17000 | ) | + | 600 | ( | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 17000 | ) | ( | 16 | + | x | ) |
去掉方程左边的一个括号:
| | 1360000 | x | + | 10200000 | × | 16 | + | 10200000 | x | + | 85000 | x | ( | 16 | + | x | ) | = | 80 | x | ( | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 17000 | ) | + | 600 | ( | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 17000 | ) | ( | 16 | + | x | ) |
去掉方程右边的一个括号:
| | 1360000 | x | + | 10200000 | × | 16 | + | 10200000 | x | + | 85000 | x | ( | 16 | + | x | ) | = | 80 | x | × | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 80 | x | × | 17000 | + | 600 | ( | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 17000 | ) | ( | 16 | + | x | ) |
方程化简为:
| | 1360000 | x | + | 163200000 | + | 10200000 | x | + | 85000 | x | ( | 16 | + | x | ) | = | 23040000 | x | x | ÷ | ( | 288000 | + | x | ) | + | 1360000 | x | + | 600 | ( | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 17000 | ) | ( | 16 | + | x | ) |
方程化简为:
| | 11560000 | x | + | 163200000 | + | 85000 | x | ( | 16 | + | x | ) | = | 23040000 | x | x | ÷ | ( | 288000 | + | x | ) | + | 1360000 | x | + | 600 | ( | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 17000 | ) | ( | 16 | + | x | ) |
| | 11560000 | x | ( | 288000 | + | x | ) | + | 163200000 | ( | 288000 | + | x | ) | + | 85000 | x | ( | 16 | + | x | ) | ( | 288000 | + | x | ) | = | 23040000 | x | x | + | 1360000 | x | ( | 288000 | + | x | ) | + | 600 | ( | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 17000 | ) | ( | 16 | + | x | ) | ( | 288000 | + | x | ) |
去掉方程左边的一个括号:
| | 11560000 | x | × | 288000 | + | 11560000 | x | x | + | 163200000 | ( | 288000 | + | x | ) | + | 85000 | x | ( | 16 | + | x | ) | ( | 288000 | + | x | ) | = | 23040000 | x | x | + | 1360000 | x | ( | 288000 | + | x | ) | + | 600 | ( | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 17000 | ) | ( | 16 | + | x | ) | ( | 288000 | + | x | ) |
去掉方程右边的一个括号:
| | 11560000 | x | × | 288000 | + | 11560000 | x | x | + | 163200000 | ( | 288000 | + | x | ) | + | 85000 | x | ( | 16 | + | x | ) | ( | 288000 | + | x | ) | = | 23040000 | x | x | + | 1360000 | x | × | 288000 | + | 1360000 | x | x | + | 600 | ( | 288000 | x | ÷ | ( | 288000 | + | x | ) | + | 17000 | ) | ( | 16 | + | x | ) |
方程化为一般式后,有公因式:
( x +0 )
由
x + 0 = 0
得:
x1=0
不能由因式分解法得出的解:
x2≈-138.096699 ,保留6位小数
x3≈-16.015181 ,保留6位小数
x4≈-13.903301 ,保留6位小数
有 4个解。
解程的详细方法请参阅:《方程的解法》
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