Question

292 Найти корни уравнения
а) |2x^2-3x+1|=|x^2+x-2|

Answer 1

$|f(x)|=|g(x)|Rightarrow left[array f(x)=g(x) \ f(x)=-g(x) end{array}right.$

$|2x^2-3x+1|=|x^2+x-2| \ left[array 2x^2-3x+1=x^2+x-2 \ 2x^2-3x+1=-(x^2+x-2) end{array}right. \ left[array 2x^2-3x+1=x^2+x-2 \ 2x^2-3x+1=-x^2-x+2 end{array}right. \ left[array x^2-4x+3=0 \ 3x^2-2x-1=0 end{array}right. \ left[array (x-1)(x-3)=0 \ (x-1)(3x+1)=0 end{array}right. Rightarrow left[array x_1=1; x_2=3 \ x_3=1 ; x_4=- frac{1}{3} end{array}right.$

Ответ: -1/3; 1; 3