Question

(х-2)²+(х+2)²-2(х-2)²=16​

Answer 1

Ответ:

$\underline{(x-2)^2}+(x+2)^2\underline {-2(x-2)^2}=16\\\\(x+2)^2-(x-2)^2=16\\\\x^2+4x+4-(x^2-4x+4)=16\\\\8x=16\\\\x=2$

Answer 2

Let's solve the equation step by step:

(х-2)² + (х+2)² - 2(х-2)² = 16

First, let's simplify the equation:

(х-2)² is the same as (х-2)(х-2) = х² - 4х + 4 (х+2)² is the same as (х+2)(х+2) = х² + 4х + 4 2(х-2)² = 2(х² - 4х + 4) = 2х² - 8х + 8

Now, let's substitute these simplified expressions back into the equation:

х² - 4х + 4 + х² + 4х + 4 - (2х² - 8х + 8) = 16

Now, simplify further:

х² - 4х + 4 + х² + 4х + 4 - 2х² + 8х - 8 = 16

Combine like terms:

2х² + 8 = 16

Subtract 8 from both sides:

2х² = 8

Now, divide by 2 to isolate х²:

х² = 4

To solve for х, take the square root of both sides:

х = ±√4

So, there are two solutions:

х = 2 and х = -2