Question

(2х-1)⁴+(2х-1)²-2=0​

Answer 1

Ответ:x=0

X=1

Объяснение:

Answer 2

To solve the equation (2x - 1)^4 + (2x - 1)^2 - 2 = 0, you can use a substitution to make it more manageable. Let's use a substitution:

Let y = (2x - 1)^2

Now, the equation becomes:

y^2 + y - 2 = 0

This is a quadratic equation in terms of y, and you can solve it using the quadratic formula:

y = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = 1, and c = -2. Plug these values into the formula:

y = (-1 ± √(1² - 4(1)(-2))) / (2(1))

y = (-1 ± √(1 + 8)) / 2

y = (-1 ± √9) / 2

Now, you have two possible solutions for y:

1. y = (-1 + 3) / 2 = 2/2 = 1
2. y = (-1 - 3) / 2 = -4/2 = -2

Now, remember that we substituted y for (2x - 1)^2. So, we need to solve for x for each of these values of y:

1. (2x - 1)^2 = 1 Take the square root of both sides: 2x - 1 = ±1 For 2x - 1 = 1: 2x = 2 x = 1

   For 2x - 1 = -1: 2x = 0 x = 0

2. (2x - 1)^2 = -2 There are no real solutions for this case because the square of a real number is always non-negative, so there are no real values of x that satisfy this equation.

So, the real solutions for the original equation are x = 0 and x = 1.