(x+2)(x+3)(x+8)(x+12)=4x^2 x^2-7|x|+12=0 x^2+|x-1|=2

Предыдущий
вопрос Следующий
вопрос

The given equations are:

1) (x + 2)(x + 3)(x + 8)(x + 12) = 4x^2

2) x^2 - 7| x | + 12 = 0

3) x^2 + | x - 1 | = 2

For equation 1:

Expanding the equation, we get:

x^4 + 25x^3 + 214x^2 + 768x = 4x^2

Rearranging and simplifying, we get:

x^4 + 25x^3 + 210x^2 + 768x = 0

This is the solution for equation 1.

For equation 2:

This is a quadratic equation which can be simplified by assuming different values for x:

For x ≥ 0:

x^2 - 7x + 12 = 0

Factoring, we get:

(x - 3)(x - 4) = 0

So, x = 3 or x = 4

For x < 0:

x^2 - 7(-x) + 12 = 0

x^2 + 7x + 12 = 0

Factoring, we get:

(x + 3)(x + 4) = 0

So, x = -3 or x = -4

Therefore, x = -4, -3, 3, or 4 are the solutions for equation 2.

For equation 3:

We can rewrite the equation as:

x^2 + (x - 1) = 2

Simplifying:

x^2 + x - 1 = 2

x^2 + x - 3 = 0

Factoring this quadratic equation gives us:

(x + 2)(x - 1) = 0

So, x = -2 or x = 1 are the solutions for equation 3.