Question

(8х^2-3х+1)^2=32х^2-12х+1
Решите уравнение

Answer 1

$(8x^2-3x+1)^2=32x^2-12x+1 \(8x^2-3x+1)^2=4(8x^2-3x)+1 \8x^2-3x=y \(y+1)^2=4y+1 \y^2+2y+1=4y+1 \y^2-2y=0 \y(y-2)=0 \y_1=0 \y-2=0 \y_2=2 \8x^2-3x=0 \x(8x-3)=0 \x_1=0 \x_2= frac{3}{8} =0,375 \8x^2-3x=2 \8x^2-3x-2=0 \D=9+64=73 \x_{3,4}= frac{3 pm sqrt{73}}{16}$