Question

Giải phương trình:

a) \(\sqrt{31x^2+57x+2}=5x+4\)

b)\(\sqrt{3^2+4x}=\sqrt{2x+9}\)

Answer 1

a.

\(\sqrt{31x^2+57x+2}=5x+4\)

\(\Leftrightarrow\left\{{}\begin{matrix}5x+4\ge0\\31x^2+57x+2=\left(5x+4\right)^2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-\dfrac{4}{5}\\6x^2+17x-14=0\end{matrix}\right.\)

\(\Rightarrow x=\dfrac{2}{3}\)

b.

\(\sqrt{3x^2+4x}=\sqrt{2x+9}\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x+9\ge0\\3x^2+4x=2x+9\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-\dfrac{9}{2}\\3x^2+2x-9=0\end{matrix}\right.\)

\(\Leftrightarrow x=\dfrac{-1\pm2\sqrt{7}}{3}\)