Question

Giải phương trình

1.\(\sqrt{x^2-x+2}\) -2\(\sqrt{x-2}\) +2=\(\sqrt{x+1}\)

2.\(\sqrt{x^2+10x+21}\)=3\(\sqrt{x+3}\) +2\(\sqrt{x+7}\) -6

Answer 1

1.Sai đề

2. Đặt \(\left\{{}\begin{matrix}a=\sqrt{x+3}\\b=\sqrt{x+7}\end{matrix}\right.\)

Pt tt: \(ab=3a+2b-6\)

\(\Leftrightarrow\left(a-2\right)\left(b-3\right)=0\)

\(\Leftrightarrow\)\(\left[{}\begin{matrix}a=2\\b=3\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x+3}=2\\\sqrt{x+7}=3\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)

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