Question

(х-3)² + (х-4)² - (х-5)² - х =24

Answer 1

(х-3)² + (х-4)² - (х-5)² - х =24

x² - 6x + 9 + x² - 8x + 16 - x² + 10x - 25 - x -24 = 0

x² -5x -24 = 0

D = 25 + 96 = 121

x12 = (5 +- 11)/2 = -3   8

Ответ x={-3, 8}

Answer 2

To solve the equation (x-3)² + (x-4)² - (x-5)² - x = 24, we can simplify it and then solve for x.

Expanding the squares, we have:

(x - 3)² + (x - 4)² - (x - 5)² - x = 24 (x - 3)(x - 3) + (x - 4)(x - 4) - (x - 5)(x - 5) - x = 24 (x² - 6x + 9) + (x² - 8x + 16) - (x² - 10x + 25) - x = 24 x² - 6x + 9 + x² - 8x + 16 - x² + 10x - 25 - x = 24 x² - x² + x² - 6x - 8x + 10x - x - 6 + 9 + 16 - 25 - 24 = 0 -5x - x + 10 = 0 -6x + 10 = 0 -6x = -10 x = -10 / -6 x = 5/3

Therefore, the solution to the equation is x = 5/3 or approximately 1.67.