Question

Решить уравнение х4+2х2-8=0 распишите все уравнение подробнее

Answer 1

Х4+2х2-8=0
х3(х+2х2-8=0
х3=0 2х2-х-8=0 дальше дискриминант решаем

Answer 2

Solving the Equation x^4 + 2x^2 - 8 = 0

To solve the equation x^4 + 2x^2 - 8 = 0, we can use a substitution to simplify the equation and then solve for the variable.

First, let's make a substitution to simplify the equation. Let's set u = x^2. This means that u^2 = (x^2)^2 = x^4. With this substitution, the equation becomes u^2 + 2u - 8 = 0.

Now, we can solve for u using the quadratic formula, where a = 1, b = 2, and c = -8.

The quadratic formula is given by: u = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values, we get: u = (-2 ± √(2^2 - 4*1*(-8))) / (2*1) u = (-2 ± √(4 + 32)) / 2 u = (-2 ± √36) / 2 u = (-2 ± 6) / 2

So, we have two possible values for u: u = (-2 + 6) / 2 = 4 / 2 = 2 u = (-2 - 6) / 2 = -8 / 2 = -4

Now that we have the values for u, we can substitute back to find the values for x.

For u = 2: x^2 = 2 Taking the square root of both sides, we get: x = ±√2

For u = -4: x^2 = -4 This has no real solutions, as the square of a real number cannot be negative.

Therefore, the solutions to the equation x^4 + 2x^2 - 8 = 0 are: x = ±√2