Question

(x-2) 4 - (x-2) 2=6 решиту уравнение

Answer 1

(х-2)*4-(х-2)*2=6
4х-8-2х+4=6
2х=6+8-4
2х=10
х=10:2
х=5

Answer 2

To solve the equation, let's simplify it first:

(x - 2)^4 - (x - 2)^2 = 6

Now, we can use a substitution to simplify it further. Let's denote a new variable y = (x - 2)^2:

y^2 - y = 6

Now, it's a quadratic equation in terms of y. Let's rearrange it:

y^2 - y - 6 = 0

Now, we can factor the quadratic equation:

(y - 3)(y + 2) = 0

Now, set each factor to zero and solve for y:

1. y - 3 = 0 => y = 3
2. y + 2 = 0 => y = -2

But remember that y = (x - 2)^2, so we need to substitute back in for y:

1. (x - 2)^2 = 3 Taking the square root of both sides: x - 2 = ±√3 x = 2 ± √3

2. (x - 2)^2 = -2 There are no real solutions for this case since you cannot take the square root of a negative number and get a real result.

So, the solutions for the equation are: x = 2 + √3 x = 2 - √3