Question

Решите уравнение также объяснить как.

Answer 1

(x-2)²(x-3) = 12(x-2) Сокращаем (x-2) и остаётся:
x-2≠0 x≠2
(x-2)(x-3) = 12
 x²-2x-3x+6 = 12
x²-5x+6-12=0
x²-5x-6 = 0

D = 25+24=49

x1 = (5+√49)/2 = (5+7)/2=12/2=6

x2 = (5-√49)/2 = (5-7)/2 = -2/2 = -1

Answer 2

$( x-2) ^{2}( x-3)=12( x-2) \\ ( x-3)( x^{2} -4 x+4)=12 x-24 \\ x^{3} -4 x^{2} +4 x-3 x^{2} +12 x-12+24-12 x=0 \\ x^{3} -7 x^{2} +4 x+12=0 \\ x^{3} -6 x^{2} - x^{2} +6 x-2 x+12=0 \\ x^{2} ( x-6)- x( x-6)-2( x-6)=0 \\ (x-6)( x^{2} - x-2)=0 \\ x-6=0 \\ x_{1} =6 \\ x^{2} - x-2=0 \\ x_{2} = \frac{1+ \sqrt{9} }{2} = \frac{4}{2} =2 \\ x_{3} = \frac{1- \sqrt{9} }{2} = \frac{-2}{2} =-1$