Question

(х+3)²-(х-3)²=(х-2)²+(х+2)²

Answer 1

$x^{2}$ + 9 - $x^{2}$+9 = $x^{2}$ -4 + $x^{2}$ + 4
2 $x^{2}$ = 18
$x^{2}$ = 9
x=3

Answer 2

Let's simplify the equation step by step:

(х+3)² - (х-3)² = (х-2)² + (х+2)²

Expanding the square terms:

(х² + 6х + 9) - (х² - 6х + 9) = (х² - 4х + 4) + (х² + 4х + 4)

Removing the parentheses:

х² + 6х + 9 - х² + 6х - 9 = х² - 4х + 4 + х² + 4х + 4

Simplifying:

12х = 2х² + 8

Rearranging the equation:

2х² - 12х + 8 = 0

Dividing the equation by 2:

х² - 6х + 4 = 0

Now we can solve this quadratic equation by factoring or using the quadratic formula. Let's try factoring:

(х - 2)(х - 2) = 0

This gives us a repeated root of x = 2.

Therefore, the solution to the equation (х+3)²-(х-3)²=(х-2)²+(х+2)² is x = 2.