đk x<=1/8
\(< =>x^2+x+\left(1-2x\right)-\sqrt{1-8x}=0\)
\(< =>x\left(x+1\right)+\dfrac{\left(1-2x\right)^2-\sqrt{1-8x}^2}{1-2x+\sqrt{1-8x}}=0\)
\(< =>x\left(x+1\right)+\dfrac{1-4x+4x^2-1+8x}{1-2x+\sqrt{1-8x}}=0\)
\(< =>x\left(x+1\right)+\dfrac{4x\left(x+1\right)}{1-2x+\sqrt{1-8x}}=0\)
\(< =>x\left(x+1\right)\left(1+\dfrac{4}{1-2x+\sqrt{1-8x}}\right)=0\)
\(< =>\left[{}\begin{matrix}x=0\left(tm\right)\\x+1=0< =>x=-1\left(tm\right)\\1+\dfrac{4}{1-2x+\sqrt{1-8x}}=0\end{matrix}\right.\)
nhận xét \(\sqrt{1-8x}\ge0\forall x\)
\(x\le\dfrac{1}{8}< =>1-2x\ge\dfrac{3}{4}>0=>1-2x+\sqrt{1-8x}>0=>1+\dfrac{4}{1-2x+\sqrt{1-8x}}>0\)
=> phương trình \(1+\dfrac{4}{1-2x+\sqrt{1-8x}}=0\) vô nghiệm
