Решите уравнение:
1) $(x + 9)^2 - x(x + 8) = 1$;
2) $(x - 11)^2 = (x - 7)(x - 9)$;
3) $(x - 4)(x + 4) - (x + 6)^2 = -16$;
4) $(1 - 3x)^2 - x(9x - 2) = 5$.
$(x + 9)^2 - x(x + 8) = 1$
$x^2 + 18x + 81 - x^2 - 8x = 1$
18x − 8x = 1 − 81
10x = −80
x = −80 : 10
x = −8
$(x - 11)^2 = (x - 7)(x - 9)$
$x^2 - 22x + 121 = x^2 - 7x + 63 - 9x$
$x^2 - x^2 - 22x + 7x + 9x = 63 - 121$
−22x + 7x + 9x = −58
−6x = −58
$x = \frac{58}{6} = \frac{29}{3} = 9\frac{2}{3}$
$(x - 4)(x + 4) - (x + 6)^2 = -16$
$x^2 - 16 - (x^2 + 12x + 36) = -16$
$x^2 - 16 - x^2 - 12x - 36 = -16$
−12x = −16 + 16 + 36
−12x = 36
x = 36 : −12
x = −3
$(1 - 3x)^2 - x(9x - 2) = 5$
$1 - 6x + 9x^2 - 9x^2 + 2x = 5$
−6x + 2x = 5 − 1
−4x = 4
x = 4 : (−4)
x = −1
Пожауйста, оцените решение
