\(\sqrt{1-x}=\sqrt{6-x}-\sqrt{-5-2x}.\)
\(ĐK:\)\(\left\{{}\begin{matrix}x\le1.\\x\le6.\\x\le\dfrac{-5}{2}.\end{matrix}\right.\)\(\Leftrightarrow x\le\dfrac{-5}{2}.\)
\(\Leftrightarrow1-x=\left(6-x\right)-2\sqrt{\left(6-x\right)\left(-5-2x\right)}+\left(-5-2x\right).\)
\(\Leftrightarrow1-x=1-3x-2\sqrt{2x^2-7x-30}.\)
\(\Leftrightarrow2x=-2\sqrt{2x^2-7x-30}.\Leftrightarrow4x^2=\left(-2\right)^2.\left(2x^2-7x-30\right).\)
\(\Leftrightarrow4x^2=4.\left(2x^2-7x-30\right).\)
\(\Leftrightarrow4x^2=8x^2-28x-120.\)
\(\Leftrightarrow4x^2-28x-120=0.\)
\(\Leftrightarrow\left(x-10\right)\left(x+3\right)=0.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=10\left(koTM\right).\\x=-3\left(TM\right).\end{matrix}\right.\)
