Question

100 БАЛЛОВ!!! Решите уравнение (x^2+1/x^2)^2-4(x+1/x)^2+12=0 ПОДРОБНО, ПОЖАЛУЙСТА

Answer 1

(x^2+1/x^2)^-4(x+1/x)+12=0
(x^2+x^-2)^2-4(x+x^-1)^2+12=0
12+x^4+x^-4-4*x^2+x^2=0
12+x^-4-3x+x^4=0
3x=-12
x=-12/3
x=-4

Answer 2

Solving the Equation

To solve the equation (x^2 + 1/x^2)^2 - 4(x + 1/x)^2 + 12 = 0, we can follow these steps:

1. Let's start by substituting y = x + 1/x. This will help simplify the equation.

2. We can then express x^2 + 1/x^2 in terms of y using the substitution.

3. After making the substitution, we can solve for y, and then solve for x.

Substituting y = x + 1/x

By substituting y = x + 1/x, the equation becomes:

(x^2 + 1/x^2)^2 - 4y^2 + 12 = 0

Expressing x^2 + 1/x^2 in terms of y

We can express x^2 + 1/x^2 in terms of y as follows:

x^2 + 1/x^2 = y^2 - 2

Solving for y

Substituting x^2 + 1/x^2 = y^2 - 2 into the equation, we get:

(y^2 - 2)^2 - 4y^2 + 12 = 0

Expanding and simplifying this equation will give us a quadratic equation in terms of y.

Solving for x

Once we solve for y, we can then solve for x using the substitution y = x + 1/x.

Let's proceed with these steps to solve the equation.