Question

(x+3)^2+2(x-6)(x+3)+(x-6)^2=0

Answer 1

(x+3)²+2(x-6)(x+3)+(x-6)²=0
х² + 6х + 9 + (2х-12)(х+3) + х² - 12х + 36 = 0
х² + 6х + 9 + 2х² + 6х - 12х - 36 + х² - 12х + 36 =0
4х² - 12х + 9 = 0
D = 144 - 4×4×9 = √144 - 144 = √0 = 0
x = 12 ± 0 / 8 = 12/8 = 3/2 = 1 ½

Answer 2

${x}^{2} + 6x + 9 + 2 \times( {x}^{2} + 3x - 6x - 18) + {x}^{2} - 12x + 36 = 0 \\ {x}^{2} + 6x + 9 + 2 {x}^{2} - 6x - 36 + {x}^{2} - 12x + 36 = 0 \\ 4 {x}^{2} - 12x + 9 = 0$
D = b^2 - 4ac => 144 - 4*4*9 = 144 - 144 =0
Уравнение имеет один корень.
$x = \frac{ - b}{2a}$
x = 12 / 8 = 1,5