Question

a)\(\sqrt{4x-1}+\sqrt{4x^2-1}=1\)

b)\(x+4\sqrt{x+3}+2\sqrt{3-2x}=11\)

c)\(\sqrt{x}-x=1-\sqrt{2x+1}\)

d)\(\sqrt{x}+\sqrt{4-x}-2=-x\)

e)\(\sqrt{4+x}+x=\sqrt{4+12x}\)

Answer 1

a) ĐK:\(x\ge\frac{1}{2}\)

Với \(x\ge\frac{1}{2}\) thì \(\left\{{}\begin{matrix}\sqrt{4x-1}\ge1\\\sqrt{4x^2-1}\ge0\end{matrix}\right.\Rightarrow VT\ge1=VP\)

=> PT có nghiệm khi và chỉ khi \(x=\frac{1}{2}\)

b) ĐK: \(-3\le x\le\frac{3}{2}\)

\(x+4\sqrt{x+3}+2\sqrt{3-2x}=11\\ \left[\left(x+3\right)-4\sqrt{x+3}+4\right]+\left[\left(3-2x\right)-2\sqrt{3-2x}+1\right]=0\\ \left(\sqrt{x+3}-2\right)^2+\left(\sqrt{3-2x}-1\right)^2=0\)

Lập luận =>\(\left\{{}\begin{matrix}\sqrt{x+3}=2\\\sqrt{3-2x}=1\end{matrix}\right.\Leftrightarrow x=1}\)