Question

\(2x^2+8x-7\sqrt{x^2+4x+7}+20=0\)

giải pt

Answer 1

Đặt \(\sqrt{x^2+4x+7}=t>0\), ta có pt sau:

\(2\left(t^2+3\right)-7t=0\)

⇔ \(t^2-7t+6=0\Leftrightarrow\left(t-2\right)\left(2t-3\right)=0\)

⇔\(\left[{}\begin{matrix}t=2\\t=\frac{3}{2}\end{matrix}\right.\)⇔\(\left[{}\begin{matrix}x^2+4x+7=4\\x^2+4x+7=\frac{9}{4}\end{matrix}\right.\)⇔\(\left[{}\begin{matrix}\left[{}\begin{matrix}x=-1\\x=-3\end{matrix}\right.\\x=\frac{\pm\sqrt{79}-4}{2}\end{matrix}\right.\)

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