Question

\(\sqrt{x+3}+\sqrt{2-x}-\sqrt{6-x-x^2}=1\)
Gpt

Answer 1

ĐK: \(-3\le x\le2\)

Đặt: \(\left\{{}\begin{matrix}\sqrt{x+3}=a\\\sqrt{2-x}=b\end{matrix}\right.\left(a,b\ge0\right)\)

\(PT\Leftrightarrow a+b-ab=1\)

\(\Leftrightarrow\left(a-1\right)\left(1-b\right)=0\)

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

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