Question

(x-2) (12-x)=9 Решить уровнение

Answer 1

X1= 11

X2= 3

$(x - 2)(12 - x) = 9$

$12x - x {}^{2} - 24 + 2x = 9$

$14x - x {}^{2} - 24 = 9$

$14x - x {}^{2} - 24 - 9 = 0$

$- x {}^{2} + 14x - 33 = 0$

Меняем знаки:

$x {}^{2} - 14x + 33 = 0$

По формуле дискриминанта:

а= 1; b= -14; c= 33

$x = \frac{ - ( - 14) + - \sqrt{( - 14) {}^{2} } - 4 \times 1 \times 33 }{2 \times 1}$

$x = \frac{14 + - \sqrt{196 - 132} }{2}$

$x = \frac{14 + - \sqrt{64} }{2}$

$x = \frac{14 + - 8}{2}$

$x1 = \frac{14 +8 }{2} = 11$

$x2 = \frac{14 - 8}{2} = 3$

Проверка:

(11-2)(12-11)=9

9*1=9

9=9 ✓

(3-2)(12-3)=9

1*9=9

9=9 ✓

Answer 2

(x-2)*(12-x)=9

12х-х²-24+2х=9

-х²+14х-33=0

D=b^{2} -4ac=14^{2}-4*(-1)*(-33)=196-132=64

$x_{1,2}=\frac{-b+-\sqrt{D}}{2a}$

$x_{1} =\frac{-14+\sqrt{64} }{2*(-1)} =\frac{-14+8}{-2} =\frac{-6}{-2}=3$

$x_{2}=\frac{-14-\sqrt{64} }{2*(-1)}=\frac{-14-8}{-2} =\frac{-22}{-2}=11$

ответ: х₁=3, х₂=11