Question

3) (x+3)2 + (x – 4)2 = 2 (4 – x)(x + 3). !!!!!!!

Answer 1

(х+3)²+(х-4)²=2(4-х)(х+3)

х²+6х+9+х²-8х+16=2(4х+12-х²-3х)

2х²-2х+25‐2(х+12-х²)=0

2х²-2х+25-2х-24+2х²=0

4х²-4х+1=0

(2x-1)²=0

2x-1=0; 2x=1; x=1/2.

Answer 2

Ответ:

Смотри решение на фото

Answer 3

To solve the equation (x+3)^2 + (x-4)^2 = 2(4-x)(x+3), you can follow these steps:

1. Expand and simplify both sides of the equation: (x+3)^2 + (x-4)^2 = 2(4-x)(x+3)

   Expand the squares on the left side: x^2 + 6x + 9 + x^2 - 8x + 16 = 2(4-x)(x+3)

   Simplify further: 2x^2 + 6x + 25 = 2(4-x)(x+3)

2. Distribute on the right side of the equation: 2x^2 + 6x + 25 = 8(x+3) - 2x(x+3)

   Distribute the 8 and -2x on the right side: 2x^2 + 6x + 25 = 8x + 24 - 2x^2 - 6x

3. Combine like terms: 2x^2 + 6x + 25 = 8x + 24 - 2x^2 - 6x

   Rearrange the terms: 2x^2 + 6x + 2x^2 + 6x = 24 - 25

   Combine like terms: 4x^2 + 12x - 1 = 0

4. Now, you have a quadratic equation in standard form. To solve for x, you can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

   In this case, a = 4, b = 12, and c = -1.

   x = (-12 ± √(12² - 4 * 4 * (-1))) / (2 * 4)

   x = (-12 ± √(144 + 16)) / 8

   x = (-12 ± √160) / 8

   x = (-12 ± 4√10) / 8

   Simplify further by factoring out a common factor of 4: x = (4(-3 ± √10)) / 8

   Reduce the fraction by dividing both the numerator and denominator by 4: x = (-3 ± √10) / 2

So, the solutions to the equation are: x = (-3 + √10) / 2 x = (-3 - √10) / 2