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Work: Find the solution of equation （x+1)(x+2)-(x-3)(x+6) = 0 .
Question type: Equation
Solution:Original question:| | ( | x | + | 1 | ) | ( | x | + | 2 | ) | − | ( | x | − | 3 | ) | ( | x | + | 6 | ) | = | 0 |
Remove the bracket on the left of the equation:
| Left side of the equation = | x | ( | x | + | 2 | ) | + | 1 | ( | x | + | 2 | ) | − | ( | x | − | 3 | ) | ( | x | + | 6 | ) |
| = | x | x | + | x | × | 2 | + | 1 | ( | x | + | 2 | ) | − | ( | x | − | 3 | ) | ( | x | + | 6 | ) |
| = | x | x | + | 2 | x | + | 1 | x | + | 1 | × | 2 | − | ( | x | − | 3 | ) | ( | x | + | 6 | ) |
| = | x | x | + | 2 | x | + | 1 | x | + | 2 | − | ( | x | − | 3 | ) | ( | x | + | 6 | ) |
| = | x | x | + | 3 | x | + | 2 | − | ( | x | − | 3 | ) | ( | x | + | 6 | ) |
| = | x | x | + | 3 | x | + | 2 | − | x | ( | x | + | 6 | ) | + | 3 | ( | x | + | 6 | ) |
| = | x | x | + | 3 | x | + | 2 | − | x | x | − | x | × | 6 | + | 3 | ( | x | + | 6 | ) |
| = | x | x | − | 3 | x | + | 2 | − | x | x | + | 3 | ( | x | + | 6 | ) |
| = | x | x | − | 3 | x | + | 2 | − | x | x | + | 3 | x | + | 3 | × | 6 |
| = | x | x | − | 3 | x | + | 2 | − | x | x | + | 3 | x | + | 18 |
The equation is transformed into :
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