总述：本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业：求方程 82560000+6000(1-t)*2000(1+3t) = 12000(1+t)*[10000-2000(1+3t)] 的解.
题型：方程
解:原方程：| | 82560000 | + | 6000 | ( | 1 | − | t | ) | × | 2000 | ( | 1 | + | 3 | t | ) | = | 12000 | ( | 1 | + | t | ) | ( | 10000 | − | 2000 | ( | 1 | + | 3 | t | ) | ) |
| 方程左边 = | 82560000 | + | 12000000 | ( | 1 | − | t | ) | ( | 1 | + | 3 | t | ) |
方程化为：
| | 82560000 | + | 12000000 | ( | 1 | − | t | ) | ( | 1 | + | 3 | t | ) | = | 12000 | ( | 1 | + | t | ) | ( | 10000 | − | 2000 | ( | 1 | + | 3 | t | ) | ) |
去掉方程左边的括号：
| 方程左边 = | 82560000 | + | 12000000 | × | 1 | ( | 1 | + | 3 | t | ) | − | 12000000 | t | ( | 1 | + | 3 | t | ) |
| = | 82560000 | + | 12000000 | ( | 1 | + | 3 | t | ) | − | 12000000 | t | ( | 1 | + | 3 | t | ) |
| = | 82560000 | + | 12000000 | × | 1 | + | 12000000 | × | 3 | t | − | 12000000 | t | ( | 1 | + | 3 | t | ) |
| = | 82560000 | + | 12000000 | + | 36000000 | t | − | 12000000 | t | ( | 1 | + | 3 | t | ) |
| = | 94560000 | + | 36000000 | t | − | 12000000 | t | ( | 1 | + | 3 | t | ) |
| = | 94560000 | + | 36000000 | t | − | 12000000 | t | × | 1 | − | 12000000 | t | × | 3 | t |
| = | 94560000 | + | 36000000 | t | − | 12000000 | t | − | 36000000 | t | t |
| = | 94560000 | + | 24000000 | t | − | 36000000 | t | t |
方程化为：
| | 94560000 | + | 24000000 | t | − | 36000000 | t | t | = | 12000 | ( | 1 | + | t | ) | ( | 10000 | − | 2000 | ( | 1 | + | 3 | t | ) | ) |
去掉方程右边的括号：
| 方程右边 = | 12000 | × | 1 | ( | 10000 | − | 2000 | ( | 1 | + | 3 | t | ) | ) | + | 12000 | t | ( | 10000 | − | 2000 | ( | 1 | + | 3 | t | ) | ) |
| = | 12000 | ( | 10000 | − | 2000 | ( | 1 | + | 3 | t | ) | ) | + | 12000 | t | ( | 10000 | − | 2000 | ( | 1 | + | 3 | t | ) | ) |
| = | 12000 | × | 10000 | − | 12000 | × | 2000 | ( | 1 | + | 3 | t | ) | + | 12000 | t | ( | 10000 | − | 2000 | ( | 1 | + | 3 | t | ) | ) |
| = | 120000000 | − | 24000000 | ( | 1 | + | 3 | t | ) | + | 12000 | t | ( | 10000 | − | 2000 | ( | 1 | + | 3 | t | ) | ) |
| = | 120000000 | − | 24000000 | × | 1 | − | 24000000 | × | 3 | t | + | 12000 | t | ( | 10000 | − | 2000 | ( | 1 | + | 3 | t | ) | ) |
| = | 120000000 | − | 24000000 | − | 72000000 | t | + | 12000 | t | ( | 10000 | − | 2000 | ( | 1 | + | 3 | t | ) | ) |
| = | 96000000 | − | 72000000 | t | + | 12000 | t | ( | 10000 | − | 2000 | ( | 1 | + | 3 | t | ) | ) |
| = | 96000000 | − | 72000000 | t | + | 12000 | t | × | 10000 | − | 12000 | t | × | 2000 | ( | 1 | + | 3 | t | ) |
| = | 96000000 | − | 72000000 | t | + | 120000000 | t | − | 24000000 | t | ( | 1 | + | 3 | t | ) |
| = | 96000000 | + | 48000000 | t | − | 24000000 | t | ( | 1 | + | 3 | t | ) |
| = | 96000000 | + | 48000000 | t | − | 24000000 | t | × | 1 | − | 24000000 | t | × | 3 | t |
| = | 96000000 | + | 48000000 | t | − | 24000000 | t | − | 72000000 | t | t |
| = | 96000000 | + | 24000000 | t | − | 72000000 | t | t |
方程化为：
| | 94560000 | + | 24000000 | t | − | 36000000 | t | t | = | 96000000 | + | 24000000 | t | − | 72000000 | t | t |
方程可以化为：
| | 94560000 | + | 24000000 | t | − | 36000000 | t | t | = | 96000000 | + | 24000000 | t | − | 72000000 | t | t |
方程化为一般式后，用因式分解法化为：
( 5t + 1 )( 5t - 1 )=0
由
5t + 1 = 0
5t - 1 = 0
得：
有 2个解。
解一元二次方程的详细方法请参阅：《一元二次方程的解法》
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