(x-6)^2 + (x+8)^2 = 2x^2Expanding both sides:(x^2 - 12x + 36) + (x^2 + 16x + 64) = 2x^2Combining like terms:2x^2 + 4x^2 - 12x + 16x + 36 + 64 = 2x^26x^2 + 4x - 12x + 16x + 100 = 2x^26x^2 + 8x + 100 = 2x^26x^2 - 2x^2 + 8x = -1004x^2 + 8x = -1004(x^2 + 2x) = -100x^2 + 2x = -25x^2 + 2x + 25 = 0(x + 5)^2 = 0x + 5 = 0x = -5
Ответ: x = -5
(x-6)^2 + (x+8)^2 = 2x^2
Expanding both sides:
(x^2 - 12x + 36) + (x^2 + 16x + 64) = 2x^2
Combining like terms:
2x^2 + 4x^2 - 12x + 16x + 36 + 64 = 2x^2
6x^2 + 4x - 12x + 16x + 100 = 2x^2
6x^2 + 8x + 100 = 2x^2
6x^2 - 2x^2 + 8x = -100
4x^2 + 8x = -100
4(x^2 + 2x) = -100
x^2 + 2x = -25
x^2 + 2x + 25 = 0
(x + 5)^2 = 0
x + 5 = 0
x = -5
Ответ: x = -5