a/ ĐKXĐ: \(0\le x\le1\)
Đặt \(\sqrt{x}+\sqrt{1-x}=a>0\Rightarrow2\sqrt{x-x^2}=a^2-1\)
\(\Rightarrow1+\frac{a^2-1}{2}=a\Leftrightarrow a^2-2a+1=0\Rightarrow a=1\)
\(\Rightarrow\sqrt{x}+\sqrt{1-x}=1\)
\(\Leftrightarrow1+2\sqrt{x-x^2}=1\)
\(\Rightarrow x-x^2=0\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
b/ Đặt \(\sqrt{x+5}=a\ge0\Rightarrow a^2-x=5\)
\(x^2+a=a^2-x\)
\(\Leftrightarrow\left(x-a\right)\left(x+a\right)+x+a=0\)
\(\Leftrightarrow\left(x+a\right)\left(x-a+1\right)=0\Rightarrow\left[{}\begin{matrix}a=-x\\a=x+1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\sqrt{x+5}=-x\left(x\le0\right)\\\sqrt{x+5}=x+1\left(x\ge-1\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x+5=x^2\\x+5=x^2+2x+1\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x^2-x-5=0\\x^2+x-4=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{1+\sqrt{21}}{2}\left(l\right)\\x=\frac{1-\sqrt{21}}{2}\\x=\frac{-1+\sqrt{17}}{2}\\x=\frac{-1-\sqrt{17}}{2}\left(l\right)\end{matrix}\right.\)
