Решите уравнение:
а) (х - 7)2 + 3 = (х - 2)(х + 2); б) (х + 6)2 - (х - 5)(х + 5) = 79;
в) (2х - 3)2 - (7 - 2х)2 = 2; г) (5x - 1)2 - (1 - 3x)2 = 16x(x - 3).
Решение:
а) (х - 7)2 + 3 = (х - 2)(х + 2) => x2 - 14x + 49 + 3 = x2 - 4 => 14x = 56 => x = 4;
б) (х + 6)2 - (х - 5)(х + 5) = 79 => x2 + 12x + 36 - x2 + 25 = 79 => 12x = 18 => x = 1,5;
в) (2х - 3)2 - (7 - 2х)2 = 2 => 4x2 - 12x + 9 - 49 + 28x - 4x2 = 2 => 16x = 42 => x = 2 5/8;
г) (5x - 1)2 - (1 - 3x)2 = 16x • (x - 3) => 25x2 - 10x + 1 - 1 + 6x - 9x2 = 16x2 - 48x => 44x = 0 => x = 0.
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