Question

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

Answer 1

Ответ:

(х+3)²+(4-х)²=2(х-4)(х+3)

х²+6х+9+16-8х+х²=2(х²-4х+3х-12)

2х²-2х+25=2х²-8х+6х-24

2х²-2х+25=2х²-2х-24

2х²-2х+25-2х²+2х+24=0

49=0

Ответ: решений нет.

Answer 2

Let's simplify the given equation step by step:

1. Expand the left side of the equation: (x + 3)^2 + (4 - x)^2 = 2(x - 4)(x + 3)

2. Square both terms on the left side: (x^2 + 6x + 9) + (16 - 8x + x^2) = 2(x^2 - 4x + 3x - 12)

3. Combine like terms on both sides of the equation: x^2 + 6x + 9 + 16 - 8x + x^2 = 2(x^2 - x - 12)

4. Simplify the equation further: 2x^2 + 25 = 2(x^2 - x - 12)

5. Distribute the 2 on the right side: 2x^2 + 25 = 2x^2 - 2x - 24

6. Now, let's isolate the variable terms on one side of the equation: 2x^2 - 2x^2 + 2x - 25 + 24 = 0

7. Simplify further: 2x = -1

8. Finally, divide by 2 to solve for x: x = -1/2

So, the solution to the equation is x = -1/2.