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A có nghĩa khi mẫu phân số khác 0 và biểu thức trong căn dương;

\(\Leftrightarrow\hept{\begin{cases}x\ge0\\\sqrt{x}-1\ne0\\\sqrt{x}^2-\sqrt{x}+1\ne0\end{cases}\Leftrightarrow\hept{\begin{cases}x\ge0\\\sqrt{x}\ne1\\\forall x\end{cases}}}\Leftrightarrow\hept{\begin{cases}x\ge0\\x\ne1\end{cases}}\)

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bạn chỉ cần cố gắng là làm được

Vì \(0\le x\le\frac{1}{2}\Rightarrow0\le2x\le1\Rightarrow-1\le-2x\le0\)

\(1-1\le1-2x\le1\Rightarrow0\le x\left(1-2x\right)\le\frac{1}{2}\)

\(0\le M\le\frac{1}{2}\Rightarrow M_{max}=\frac{1}{2}\)

Điều kiện để hệ có nghiệm duy nhất là \(\frac{1}{a}\ne\frac{-1}{1}\Leftrightarrow a\ne-1\)