Question

2(x-2)4-5(x-2)2+2=0​

Answer 1

2(x-2)4-5(x-2)2+2=0​

2(4х-8) - 5(2х-4)+2=0

8х-16-10х+20+2=0

-2х=-6

х = 3

проверяем подставив значение х

2(3-2)4-5(3-2)2+2=0​

2*4-5*2+2=0

8-10+2=0

0=0

Ответ: х=3.

Answer 2

To solve the quadratic equation 2(x-2)^4 - 5(x-2)^2 + 2 = 0, we can use a substitution to simplify the equation. Let's substitute (x-2)^2 with a new variable, say u. Therefore, let u = (x-2)^2.

Now, we can rewrite the equation in terms of u:

2u^2 - 5u + 2 = 0.

This is a quadratic equation in u. To solve it, we can use factoring, completing the square, or the quadratic formula. In this case, let's use factoring:

2u^2 - 5u + 2 = 0 (2u - 1)(u - 2) = 0.

Now we can solve for u:

2u - 1 = 0 or u - 2 = 0.

Solving these equations gives us:

2u = 1 or u = 2.

Dividing the first equation by 2:

u = 1/2 or u = 2.

Now we substitute back x-2 for u:

(x-2)^2 = 1/2 or (x-2)^2 = 2.

Taking the square root of both sides:

x - 2 = ±√(1/2) or x - 2 = ±√2.

Solving for x:

x = 2 ± √(1/2) or x = 2 ± √2.

Therefore, the solutions to the given quadratic equation are:

x = 2 + √(1/2), x = 2 - √(1/2), x = 2 + √2, and x = 2 - √2.