Решите уравнение:
а) $(x - 7)^2 + 3 = (x - 2)(x + 2)$;
б) $(x + 6)^2 - (x - 5)(x + 5) = 79$;
в) $(2x - 3)^2 - (7 - 2x)^2 = 2$;
г) $(5x - 1)^2 - (1 - 3x)^2 = 16x(x - 3)$.
$(x - 7)^2 + 3 = (x - 2)(x + 2)$
$x^2 - 14x + 49 + 3 = x^2 - 4$
$x^2 - 14x - x^2 = -4 - 49 - 3$
−14x = −56
x = 4
$(x + 6)^2 - (x - 5)(x + 5) = 79$
$x^2 + 12x + 36 - (x^2 - 25) = 79$
$x^2 + 12x + 36 - x^2 + 25 = 79$
12x = 79 − 36 − 25
12x = 18
$x = \frac{18}{12} = \frac{3}{2} = 1,5$
$(2x - 3)^2 - (7 - 2x)^2 = 2$
$4x^2 - 12x + 9 - (49 - 28x) + 4x^2 = 2$
$4x^2 - 12x + 9 - 49 + 28x - 4x^2 = 2$
16x = 2 − 9 + 49
16x = 42
$x = \frac{42}{16} = \frac{21}{8} = 2,625$
$(5x - 1)^2 - (1 - 3x)^2 = 16x(x - 3)$
$25x^2 - 10x + 1 - (1 - 6x + 9x^2) = 16x^2 - 48x$
$25x^2 - 10x + 1 - 1 + 6x - 9x^2 - 16x^2 + 48x = 0$
44x = 0
x = 0
Пожауйста, оцените решение
