Question

$8 {x}^{3} - 8 {x}^{2} + 1 = 0$

Answer 1

$8x^3-8x^2+1=0; (2x)^3-2(2x)^2+1=0; 2x=t; t^3-2t^2+1=0; (t^3-t^2)-(t^2-1)=0; t^2(t-1)-(t-1)(t+1)=0; (t-1)(t^2-t-1)=0;$

1) t-1=0; t=1; x=1/2

2) $t^2-t-1=0; t=frac{1pmsqrt{5}}{2}; x=frac{1pm sqrt{5}}{4}$

Ответ: ${frac{1}{2}; frac{1pmsqrt{5}}{4}}$