Question

(x-2)²+48=(2-3x)² пжжпжпжпжпжпжп

Answer 1

Ответ:

- 2 ; 3

Объяснение:

$(x - 2) {}^{2} + 48 = (2 - 3x) {}^{2} \\ x {}^{2} - 4x + 4 + 48 = 4 - 12x + 9x {}^{2} \\ x {}^{2} - 4x + 48 = - 12x + 9x {}^{2} \\ x {}^{2} - 4x + 48 + 12x - 9x {}^{2} = 0 \\ - 8x {}^{2} + 8x + 48 = 0 | \div ( - 8) \\ x {}^{2} - x - 6 = 0 \\ D = 1 + 24 = 25 = 5 {}^{2} \\ x_{1} = \dfrac{1 - 5}{2} = - \dfrac{4}{2} = - 2 \\ x_{2} = \dfrac{1 + 5}{2} = \frac{6}{2} = 3$

Answer 2

Let's solve the equation $(x-2)^2 + 48 = (2-3x)^2$ step by step.

First, expand both sides of the equation:

$(x-2)^2 + 48 = (2-3x)^2$

Expanding the left side:

$x^2 - 4x + 4 + 48 = (2-3x)^2$

Expanding the right side:

$x^2 - 4x + 4 + 48 = 4 - 12x + 9x^2$

Now, let's simplify and collect like terms:

$x^2 - 4x + 52 = 4 - 12x + 9x^2$

To solve for x, we'll move all the terms to one side of the equation:

$x^2 - 9x^2 - 4x + 12x + 52 - 4 = 0$

Combine like terms:

$-8x^2 + 8x + 48 = 0$

Now, let's simplify the equation further by dividing all terms by -8 to make it easier to work with:

$x^2 - x - 6 = 0$

We have a quadratic equation. To solve for x, you can use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In this case, $a = 1$, $b = -1$, and $c = -6$. Plug these values into the quadratic formula:

$x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(1)(-6)}}{2(1)}$

Simplify:

$x = \frac{1 \pm \sqrt{1 + 24}}{2}$

$x = \frac{1 \pm \sqrt{25}}{2}$

Now, take the square root of 25:

$x = \frac{1 \pm 5}{2}$

Now, we have two possible solutions for x:

1. $x = \frac{1 + 5}{2} = \frac{6}{2} = 3$
2. $x = \frac{1 - 5}{2} = \frac{-4}{2} = -2$

So, the equation $(x-2)^2 + 48 = (2-3x)^2$ has two solutions: $x = 3$ and $x = -2$.