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☆1 equations
[ 1/1 Equation]
Work: Find the solution of equation (3n+1)(3n+2)(6n+3)(9n+4) = (3n+4)(3n+1)(6n+2)(9n+3) .
Question type: Equation
Solution:Original question:| | ( | 3 | n | + | 1 | ) | ( | 3 | n | + | 2 | ) | ( | 6 | n | + | 3 | ) | ( | 9 | n | + | 4 | ) | = | ( | 3 | n | + | 4 | ) | ( | 3 | n | + | 1 | ) | ( | 6 | n | + | 2 | ) | ( | 9 | n | + | 3 | ) |
Remove the bracket on the left of the equation:
| Left side of the equation = | 3 | n | ( | 3 | n | + | 2 | ) | ( | 6 | n | + | 3 | ) | ( | 9 | n | + | 4 | ) | + | 1 | ( | 3 | n | + | 2 | ) | ( | 6 | n | + | 3 | ) | ( | 9 | n | + | 4 | ) |
| = | 3 | n | × | 3 | n | ( | 6 | n | + | 3 | ) | ( | 9 | n | + | 4 | ) | + | 3 | n | × | 2 | ( | 6 | n | + | 3 | ) | ( | 9 | n | + | 4 | ) | + | 1 |
| = | 9 | n | n | ( | 6 | n | + | 3 | ) | ( | 9 | n | + | 4 | ) | + | 6 | n | ( | 6 | n | + | 3 | ) | ( | 9 | n | + | 4 | ) | + | 1 | ( | 3 | n | + | 2 | ) | ( | 6 | n | + | 3 | ) |
| = | 9 | n | n | × | 6 | n | ( | 9 | n | + | 4 | ) | + | 9 | n | n | × | 3 | ( | 9 | n | + | 4 | ) | + | 6 |
| = | 54 | n | n | n | ( | 9 | n | + | 4 | ) | + | 27 | n | n | ( | 9 | n | + | 4 | ) | + | 6 | n | ( | 6 | n | + | 3 | ) |
| = | 54 | n | n | n | × | 9 | n | + | 54 | n | n | n | × | 4 | + | 27 |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 27 | n | n |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 27 | n | n |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 243 | n | n |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 243 | n | n |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 243 | n | n |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 243 | n | n |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 243 | n | n |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 243 | n | n |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 243 | n | n |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 243 | n | n |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 243 | n | n |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 243 | n | n |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 243 | n | n |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 243 | n | n |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 243 | n | n |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 243 | n | n |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 243 | n | n |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 243 | n | n |
| = | 486 | n | n | n | n | + | 216 | n | n | n | + | 243 | n | n |
n=0
There are 1 solution(s).
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