Question

(x+2)^2+(x-2)^2=3x^2-9

Answer 1

Ответ:

Решение предоставлено на картинке

Объяснение:

Answer 2

Let's solve the equation $(x+2)^2 + (x-2)^2 = 3x^2 - 9$. First, expand and simplify the left side of the equation:

$(x+2)^2 = x^2 + 4x + 4$

$(x-2)^2 = x^2 - 4x + 4$

Now, we can rewrite the equation as:

$x^2 + 4x + 4 + x^2 - 4x + 4 = 3x^2 - 9$

Combine like terms:

$2x^2 + 8 = 3x^2 - 9$

Now, subtract $3x^2$ from both sides:

$2x^2 - 3x^2 + 8 = -9$

Simplify the equation:

$-x^2 + 8 = -9$

Subtract 8 from both sides:

$-x^2 = -9 - 8$

$-x^2 = -17$

Now, multiply both sides by -1 to isolate $x^2$:

$x^2 = 17$

Take the square root of both sides. Remember to consider both positive and negative square roots:

$x = ±√17$

So, the solutions for the equation $(x+2)^2 + (x-2)^2 = 3x^2 - 9$ are $x = √17$ and $x = -√17$.