Question

Giải phương trình:

b) (4x-1)\(\sqrt{x^{3^{ }}+1}\)=2x³+2x+1

Answer 1

ĐKXĐ: ...

Đặt \(\sqrt{x^3+1}=t\ge0\)

\(\Leftrightarrow\left(4x-1\right)t=2t^2+2x-1\)

\(\Leftrightarrow2t^2-\left(4x-1\right)t+2x-1=0\)

\(\Delta=\left(4x-1\right)^2-8\left(2x-1\right)=16x^2-24x+9=\left(4x-3\right)^2\)

\(\Rightarrow\left[{}\begin{matrix}t=\frac{4x-1+4x-3}{4}=2x-1\\t=\frac{4x-1-4x+3}{4}=\frac{1}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x^3+1}=2x-1\\\sqrt{x^3+1}=\frac{1}{2}\end{matrix}\right.\)

\(\Leftrightarrow...\)