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☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation (x+3)(x+2)(4-x)+3+x+16-4x = 0 .
Question type: Equation
Solution:Original question:| | ( | x | + | 3 | ) | ( | x | + | 2 | ) | ( | 4 | − | x | ) | + | 3 | + | x | + | 16 | − | 4 | x | = | 0 |
| Left side of the equation = | ( | x | + | 3 | ) | ( | x | + | 2 | ) | ( | 4 | − | x | ) | + | 19 | − | 3 | x |
The equation is transformed into :
| | ( | x | + | 3 | ) | ( | x | + | 2 | ) | ( | 4 | − | x | ) | + | 19 | − | 3 | x | = | 0 |
Remove the bracket on the left of the equation:
| Left side of the equation = | x | ( | x | + | 2 | ) | ( | 4 | − | x | ) | + | 3 | ( | x | + | 2 | ) | ( | 4 | − | x | ) | + | 19 | − | 3 | x |
| = | x | x | ( | 4 | − | x | ) | + | x | × | 2 | ( | 4 | − | x | ) | + | 3 | ( | x | + | 2 | ) | ( | 4 | − | x | ) | + | 19 | − | 3 | x |
| = | x | x | × | 4 | − | x | x | x | + | x | × | 2 | ( | 4 | − | x | ) | + | 3 | ( | x | + | 2 | ) | ( | 4 | − | x | ) |
| = | x | x | × | 4 | − | x | x | x | + | x | × | 2 | × | 4 | − | x | × | 2 | x |
| = | x | x | × | 4 | − | x | x | x | + | x | × | 8 | − | x | × | 2 | x | + | 3 |
| = | x | x | × | 4 | − | x | x | x | + | 5 | x | − | x | × | 2 | x | + | 3 |
| = | x | x | × | 4 | − | x | x | x | + | 5 | x | − | x | × | 2 | x | + | 3 |
| = | x | x | × | 4 | − | x | x | x | + | 5 | x | − | x | × | 2 | x | + | 3 |
| = | x | x | × | 4 | − | x | x | x | + | 5 | x | − | x | × | 2 | x | + | 3 |
| = | x | x | × | 4 | − | x | x | x | + | 5 | x | − | x | × | 2 | x | + | 12 |
| = | x | x | × | 4 | − | x | x | x | + | 17 | x | − | x | × | 2 | x | − | 3 |
| = | x | x | × | 4 | − | x | x | x | + | 17 | x | − | x | × | 2 | x | − | 3 |
| = | x | x | × | 4 | − | x | x | x | + | 17 | x | − | x | × | 2 | x | − | 3 |
| = | x | x | × | 4 | − | x | x | x | + | 11 | x | − | x | × | 2 | x | − | 3 |
The equation is transformed into :
| | x | x | × | 4 | − | x | x | x | + | 11 | x | − | x | × | 2 | x | − | 3 | = | 0 |
x≈4.149063 , keep 6 decimal places
There are 1 solution(s).
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