总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 (X+1)*(x+2)*(x+4)+(x+2)*(x+4)*x+(x+1)*(x+4)*x = x*(x+1)*(x+2) 的解.
题型:方程
解:原方程:| | ( | X | + | 1 | ) | ( | X | + | 2 | ) | ( | X | + | 4 | ) | + | ( | X | + | 2 | ) | ( | X | + | 4 | ) | X | + | ( | X | + | 1 | ) | ( | X | + | 4 | ) | X | = | X | ( | X | + | 1 | ) | ( | X | + | 2 | ) |
去掉方程左边的括号:
| 方程左边 = | X | ( | X | + | 2 | ) | ( | X | + | 4 | ) | + | 1 | ( | X | + | 2 | ) | ( | X | + | 4 | ) | + | ( | X | + | 2 | ) | ( | X | + | 4 | ) | X | + | ( | X | + | 1 | ) | ( | X | + | 4 | ) | X |
| = | X | X | ( | X | + | 4 | ) | + | X | × | 2 | ( | X | + | 4 | ) | + | 1 | ( | X | + | 2 | ) | ( | X | + | 4 | ) | + | ( | X | + | 2 | ) | ( | X | + | 4 | ) | X |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | ( | X | + | 4 | ) | + | 1 | ( | X | + | 2 | ) | ( | X | + | 4 | ) |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | X | × | 2 | × | 4 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | X | × | 8 | + | 1 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 8 | X | + | 1 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 8 | X | + | 1 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 8 | X | + | 1 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 8 | X | + | 1 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 12 | X | + | 1 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 12 | X | + | 1 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 12 | X | + | 1 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 14 | X | + | 1 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 14 | X | + | 1 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 14 | X | + | 1 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 14 | X | + | 1 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 14 | X | + | 1 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 22 | X | + | 1 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 22 | X | + | 1 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 22 | X | + | 1 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 22 | X | + | 1 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 22 | X | + | 1 |
| = | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 26 | X | + | 1 |
方程化为:
| | X | X | X | + | X | X | × | 4 | + | X | × | 2 | X | + | 26 | X | + | 1 | = | X | ( | X | + | 1 | ) | ( | X | + | 2 | ) |
去掉方程右边的括号:
| 方程右边 = | X | X | ( | X | + | 2 | ) | + | X | × | 1 | ( | X | + | 2 | ) |
方程的解为:
X1≈-5.423336 ,保留6位小数
X2≈-1.621924 ,保留6位小数
X3≈-0.454740 ,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》
你的问题在这里没有得到解决?请到 热门难题 里面看看吧!