Question

[Lâm Anh Trần]

Giải phương trình

\(2x^3-\sqrt{108x+45}=x\sqrt{48x+20}-3x^2\)

Answer 1

[Nguyễn Việt Lâm]

ĐKXĐ: \(x\ge-\frac{5}{12}\)

\(2x^3-3\sqrt{12x+5}-2x\sqrt{12x+5}+3x^2=0\)

\(\Leftrightarrow x^2\left(2x+3\right)-\left(2x+3\right)\sqrt{12x+5}=0\)

\(\Leftrightarrow\left(2x+3\right)\left(x^2-\sqrt{12x+5}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+3=0\Rightarrow x=\frac{-3}{2}\left(l\right)\\x^2=\sqrt{12x+5}\left(1\right)\end{matrix}\right.\)

\(\left(1\right)\Leftrightarrow x^4-12x+5=0\)

\(\Leftrightarrow\left(x^2-2x-1\right)\left(x^2+2x+5\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=\frac{1+\sqrt{5}}{2}\\x=\frac{1-\sqrt{5}}{2}\left(l\right)\end{matrix}\right.\)