Question

Giải phương trình

\(\sqrt{x+3}-2\sqrt{2x^2+7x+3}+16=3x-\sqrt{2x+1}\)

Answer 1

ĐKXĐ: \(x\ge-\frac{1}{2}\)

\(\Leftrightarrow3x+4+2\sqrt{2x^2+7x+3}-\left(\sqrt{x+3}+\sqrt{2x+1}\right)-20=0\)

Đặt \(\sqrt{x+3}+\sqrt{2x+1}=t>0\)

\(\Rightarrow t^2=3x+4+2\sqrt{2x^2+7x+3}\)

Pt trở thành:

\(t^2-t-20=0\Rightarrow\left[{}\begin{matrix}t=5\\t=-4\left(l\right)\end{matrix}\right.\)

\(\Rightarrow\sqrt{x+3}+\sqrt{2x+1}=5\)

\(\Leftrightarrow3x+4+2\sqrt{2x^2+7x+3}=25\)

\(\Leftrightarrow2\sqrt{2x^2+7x+3}=21-3x\) (\(x\le7\))

\(\Leftrightarrow4\left(2x^2+7x+3\right)=\left(21-3x\right)^2\)

\(\Leftrightarrow x^2-154x+429=0\) (casio)