总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 90/(1+x)+90/(1+x)(1+x)+90/(1+x)(1+x)(1+x)+90/(1+x)(1+x)(1+x)(1+x)+90/(1+x)(1+x)(1+x)(1+x)(1+x)(1+x) = 300 的解.
题型:方程
解:原方程:| | 90 | ÷ | ( | 1 | + | x | ) | + | 90 | ÷ | ( | 1 | + | x | ) | × | ( | 1 | + | x | ) | + | 90 | ÷ | ( | 1 | + | x | ) | × | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 90 | ÷ | ( | 1 | + | x | ) | × | ( | 1 | + | x | ) | = | 300 |
| | 90 | + | 90 | ( | 1 | + | x | ) | + | 90 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 90 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 90 | ( | 1 | + | x | ) | = | 300 | ( | 1 | + | x | ) |
去掉方程左边的一个括号:
| | 90 | + | 90 | × | 1 | + | 90 | x | + | 90 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 90 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | = | 300 | ( | 1 | + | x | ) |
去掉方程右边的一个括号:
| | 90 | + | 90 | × | 1 | + | 90 | x | + | 90 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 90 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | = | 300 | × | 1 | + | 300 | x |
方程化简为:
| | 90 | + | 90 | + | 90 | x | + | 90 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 90 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 90 | = | 300 | + | 300 | x |
方程化简为:
| | 180 | + | 90 | x | + | 90 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 90 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 90 | ( | 1 | + | x | ) | = | 300 | + | 300 | x |
去掉方程左边的一个括号:
| | 180 | + | 90 | x | + | 90 | × | 1 | ( | 1 | + | x | ) | + | 90 | x | ( | 1 | + | x | ) | + | 90 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | = | 300 | + | 300 | x |
方程化简为:
| | 180 | + | 90 | x | + | 90 | ( | 1 | + | x | ) | + | 90 | x | ( | 1 | + | x | ) | + | 90 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | = | 300 | + | 300 | x |
去掉方程左边的一个括号:
| | 180 | + | 90 | x | + | 90 | × | 1 | + | 90 | x | + | 90 | x | ( | 1 | + | x | ) | + | 90 | ( | 1 | + | x | ) | = | 300 | + | 300 | x |
方程化简为:
| | 180 | + | 90 | x | + | 90 | + | 90 | x | + | 90 | x | ( | 1 | + | x | ) | + | 90 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | = | 300 | + | 300 | x |
方程化简为:
| | 270 | + | 180 | x | + | 90 | x | ( | 1 | + | x | ) | + | 90 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 90 | ( | 1 | + | x | ) | = | 300 | + | 300 | x |
去掉方程左边的一个括号:
| | 270 | + | 180 | x | + | 90 | x | × | 1 | + | 90 | x | x | + | 90 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | = | 300 | + | 300 | x |
方程化简为:
| | 270 | + | 180 | x | + | 90 | x | + | 90 | x | x | + | 90 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | = | 300 | + | 300 | x |
方程化简为:
| | 270 | + | 270 | x | + | 90 | x | x | + | 90 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 90 | ( | 1 | + | x | ) | = | 300 | + | 300 | x |
去掉方程左边的一个括号:
| | 270 | + | 270 | x | + | 90 | x | x | + | 90 | × | 1 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 90 | x | = | 300 | + | 300 | x |
方程化简为:
| | 270 | + | 270 | x | + | 90 | x | x | + | 90 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 90 | x | ( | 1 | + | x | ) | = | 300 | + | 300 | x |
去掉方程左边的一个括号:
| | 270 | + | 270 | x | + | 90 | x | x | + | 90 | × | 1 | ( | 1 | + | x | ) | + | 90 | x | ( | 1 | + | x | ) | = | 300 | + | 300 | x |
方程化简为:
| | 270 | + | 270 | x | + | 90 | x | x | + | 90 | ( | 1 | + | x | ) | + | 90 | x | ( | 1 | + | x | ) | + | 90 | = | 300 | + | 300 | x |
去掉方程左边的一个括号:
| | 270 | + | 270 | x | + | 90 | x | x | + | 90 | × | 1 | + | 90 | x | + | 90 | x | = | 300 | + | 300 | x |
方程化简为:
| | 270 | + | 270 | x | + | 90 | x | x | + | 90 | + | 90 | x | + | 90 | x | ( | 1 | + | x | ) | = | 300 | + | 300 | x |
方程化简为:
| | 360 | + | 360 | x | + | 90 | x | x | + | 90 | x | ( | 1 | + | x | ) | + | 90 | x | ( | 1 | + | x | ) | = | 300 | + | 300 | x |
去掉方程左边的一个括号:
| | 360 | + | 360 | x | + | 90 | x | x | + | 90 | x | × | 1 | + | 90 | x | x | = | 300 | + | 300 | x |
方程化简为:
| | 360 | + | 360 | x | + | 90 | x | x | + | 90 | x | + | 90 | x | x | + | 90 | = | 300 | + | 300 | x |
方程化简为:
| | 360 | + | 450 | x | + | 90 | x | x | + | 90 | x | x | + | 90 | x | ( | 1 | + | x | ) | = | 300 | + | 300 | x |
去掉方程左边的一个括号:
| | 360 | + | 450 | x | + | 90 | x | x | + | 90 | x | x | + | 90 | x | × | 1 | = | 300 | + | 300 | x |
方程化简为:
| | 360 | + | 450 | x | + | 90 | x | x | + | 90 | x | x | + | 90 | x | ( | 1 | + | x | ) | = | 300 | + | 300 | x |
x≈-2.286758 ,保留6位小数
有 1个解。
解一元一次方程的详细方法请参阅:《一元一次方程的解法》
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