a) \(\sqrt{1-x}+\sqrt{x+4}=3\left(Đk:-4\le x\le1\right)\)
\(1-x+x+4+2\sqrt{\left(1-x\right)\left(x+4\right)}=9\)
\(\sqrt{-x^2-3x+4}=2\)
\(-x^2-3x+4=4\)
\(x^2+3x=0\)
\(x\left(x+3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-3\left(TM\right)\\x=0\left(TM\right)\end{matrix}\right.\)
b) \(x^2+4x+5=2\sqrt{2x+3}\) \(\left(Đk:x\ge\dfrac{-3}{2}\right)\)
\(\)\(x^2+2x+1+2x+3-2\sqrt{2x+3}+1=0\)
\(\left(x+1\right)^2+\left(\sqrt{2x+3}-1\right)^2=0\)
Vì \(\left(x+1\right)^2;\left(\sqrt{2x+3}-1\right)^2\ge0\forall x\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+1=0\\2x+3=1\end{matrix}\right.\)\(\Leftrightarrow x=-1\)(TM)
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