Question

\(x^3+1=2\sqrt[3]{2x-1}\)

Answer 1

\(pt\Leftrightarrow x^3+2x=2x-1+2\sqrt[3]{2x-1}\)

Đặt \(\sqrt[3]{2x-1}=a\)

\(pt\rightarrow x^3+2x=a^3+2a\)\(\Leftrightarrow\left(x-a\right)\left(x^2+ax+a^2\right)+2\left(x-a\right)=b\)

\(\Leftrightarrow\left(x-a\right)\left[\left(x+\frac{a}{2}\right)^2+\frac{3}{4}a^2+2\right]=0\)

\(\Leftrightarrow x=a\)

\(\Rightarrow x=\sqrt[3]{2x-1}\Leftrightarrow x^3=2x-1\Leftrightarrow\left(x-1\right)\left(x^2+x-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=1\\x=\frac{-1\pm\sqrt{5}}{2}\end{cases}}\)

Answer 2

Đề bài là gì vậy bạn???