总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 1/x+2/(x+3)+3/x+6/(x+2)+2/(x+3)+1/(x+9)+3/(x+16) = 50 的解.
题型:方程
解:原方程:| | 1 | ÷ | x | + | 2 | ÷ | ( | x | + | 3 | ) | + | 3 | ÷ | x | + | 6 | ÷ | ( | x | + | 2 | ) | + | 2 | ÷ | ( | x | + | 3 | ) | + | 1 | ÷ | ( | x | + | 9 | ) | = | 50 |
| | 1 | + | 2 | ÷ | ( | x | + | 3 | ) | × | x | + | 3 | ÷ | 1 | × | 1 | + | 6 | ÷ | ( | x | + | 2 | ) | × | x | + | 2 | ÷ | ( | x | + | 3 | ) | = | 50 | x |
| | 1 | ( | x | + | 3 | ) | + | 2 | x | + | 3 | ÷ | 1 | × | 1 | ( | x | + | 3 | ) | + | 6 | ÷ | ( | x | + | 2 | ) | × | x | ( | x | + | 3 | ) | = | 50 | x | ( | x | + | 3 | ) |
去掉方程左边的一个括号:
| | 1 | x | + | 1 | × | 3 | + | 2 | x | + | 3 | ÷ | 1 | × | 1 | ( | x | + | 3 | ) | + | 6 | ÷ | ( | x | + | 2 | ) | = | 50 | x | ( | x | + | 3 | ) |
去掉方程右边的一个括号:
| | 1 | x | + | 1 | × | 3 | + | 2 | x | + | 3 | ÷ | 1 | × | 1 | ( | x | + | 3 | ) | + | 6 | ÷ | ( | x | + | 2 | ) | = | 50 | x | x | + | 50 | x | × | 3 |
方程化简为:
| | 1 | x | + | 3 | + | 2 | x | + | 3 | ( | x | + | 3 | ) | + | 6 | ÷ | ( | x | + | 2 | ) | × | x | ( | x | + | 3 | ) | + | 2 | = | 50 | x | x | + | 150 | x |
方程化简为:
| | 5 | x | + | 3 | + | 3 | ( | x | + | 3 | ) | + | 6 | ÷ | ( | x | + | 2 | ) | × | x | ( | x | + | 3 | ) | + | 1 | ÷ | ( | x | + | 9 | ) | × | x | = | 50 | x | x | + | 150 | x |
| | 5 | x | ( | x | + | 2 | ) | + | 3 | ( | x | + | 2 | ) | + | 3 | ( | x | + | 3 | ) | ( | x | + | 2 | ) | + | 6 | x | ( | x | + | 3 | ) | + | 1 | = | 50 | x | x | ( | x | + | 2 | ) | + | 150 | x | ( | x | + | 2 | ) |
去掉方程左边的一个括号:
| | 5 | x | x | + | 5 | x | × | 2 | + | 3 | ( | x | + | 2 | ) | + | 3 | ( | x | + | 3 | ) | ( | x | + | 2 | ) | + | 6 | = | 50 | x | x | ( | x | + | 2 | ) | + | 150 | x | ( | x | + | 2 | ) |
去掉方程右边的一个括号:
| | 5 | x | x | + | 5 | x | × | 2 | + | 3 | ( | x | + | 2 | ) | + | 3 | ( | x | + | 3 | ) | ( | x | + | 2 | ) | + | 6 | = | 50 | x | x | x | + | 50 | x | x | × | 2 | + | 150 | x | ( | x | + | 2 | ) |
方程化简为:
| | 5 | x | x | + | 10 | x | + | 3 | ( | x | + | 2 | ) | + | 3 | ( | x | + | 3 | ) | ( | x | + | 2 | ) | + | 6 | x | = | 50 | x | x | x | + | 100 | x | x | + | 150 | x | ( | x | + | 2 | ) |
| | 5 | x | x | ( | x | + | 9 | ) | + | 10 | x | ( | x | + | 9 | ) | + | 3 | ( | x | + | 2 | ) | ( | x | + | 9 | ) | + | 3 | ( | x | + | 3 | ) | = | 50 | x | x | x | ( | x | + | 9 | ) | + | 100 | x | x | ( | x | + | 9 | ) | + | 150 | x | ( | x | + | 2 | ) |
去掉方程左边的一个括号:
| | 5 | x | x | x | + | 5 | x | x | × | 9 | + | 10 | x | ( | x | + | 9 | ) | + | 3 | = | 50 | x | x | x | ( | x | + | 9 | ) | + | 100 | x | x | ( | x | + | 9 | ) | + | 150 | x | ( | x | + | 2 | ) |
去掉方程右边的一个括号:
| | 5 | x | x | x | + | 5 | x | x | × | 9 | + | 10 | x | ( | x | + | 9 | ) | + | 3 | = | 50 | x | x | x | x | + | 50 | x | x | x | × | 9 | + | 100 | x |
方程化简为:
| | 5 | x | x | x | + | 45 | x | x | + | 10 | x | ( | x | + | 9 | ) | + | 3 | ( | x | + | 2 | ) | = | 50 | x | x | x | x | + | 450 | x | x | x | + | 100 | x | x |
| | 5 | x | x | x | ( | x | + | 16 | ) | + | 45 | x | x | ( | x | + | 16 | ) | + | 10 | x | ( | x | + | 9 | ) | = | 50 | x | x | x | x | ( | x | + | 16 | ) | + | 450 | x | x | x | ( | x | + | 16 | ) | + | 100 |
去掉方程左边的一个括号:
| | 5 | x | x | x | x | + | 5 | x | x | x | × | 16 | + | 45 | x | = | 50 | x | x | x | x | ( | x | + | 16 | ) | + | 450 | x | x | x | ( | x | + | 16 | ) | + | 100 |
去掉方程右边的一个括号:
| | 5 | x | x | x | x | + | 5 | x | x | x | × | 16 | + | 45 | x | = | 50 | x | x | x | x | x | + | 50 | x | x | x | x | × | 16 |
方程化简为:
| | 5 | x | x | x | x | + | 80 | x | x | x | + | 45 | x | x | = | 50 | x | x | x | x | x | + | 800 | x | x | x | x | + | 450 |
去掉方程左边的一个括号:
| | 5 | x | x | x | x | + | 80 | x | x | x | + | 45 | x | x | = | 50 | x | x | x | x | x | + | 800 | x | x | x | x | + | 450 |
去掉方程右边的一个括号:
| | 5 | x | x | x | x | + | 80 | x | x | x | + | 45 | x | x | = | 50 | x | x | x | x | x | + | 800 | x | x | x | x | + | 450 |
方程化简为:
| | 5 | x | x | x | x | + | 80 | x | x | x | + | 45 | x | x | = | 50 | x | x | x | x | x | + | 800 | x | x | x | x | + | 450 |
方程的解为:
x1≈-15.941331 ,保留6位小数
x2≈-2.930338 ,保留6位小数
x3≈-1.875577 ,保留6位小数
x4≈0.087846 ,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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