Question

(x+6)(x-1)(x+3)(x+2)=12x2​

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To solve the equation $(x+6)(x-1)(x+3)(x+2) = 12x^2$, we need to first simplify the left-hand side and then set it equal to zero to solve for $x$.

1. Expand the left-hand side: $(x+6)(x-1)(x+3)(x+2) = 12x^2$

Expand each pair of factors first: $(x^2 + 6x)(x^2 + 5x - 3) = 12x^2$

Now, multiply the two quadratic expressions together: $x^4 + 5x^3 - 3x^2 + 6x^3 + 30x^2 - 18x = 12x^2$

2. Combine like terms: $x^4 + 11x^3 + 12x^2 - 18x = 12x^2$

3. Subtract $12x^2$ from both sides to set the equation equal to zero: $x^4 + 11x^3 + 12x^2 - 18x - 12x^2 = 0$

4. Simplify further: $x^4 + 11x^3 + 12x^2 - 18x - 12x^2 = 0$

$x^4 + 11x^3 - 18x = 0$

5. Now, we need to factor this equation or find its roots. Unfortunately, this quartic equation doesn't have simple integer roots, and its factorization can be quite complex. You may need to use numerical methods or a graphing calculator to find approximate solutions.

One approach is to use numerical methods like the Newton-Raphson method or software like Mathematica, MATLAB, or online equation solvers to find the roots.