Question

giải pt:a. \(4\left(x+1\right)^2+\left(2x+1\right)^2-8\left(x-1\right)\left(x+1\right)=11\)

b. \(x-\frac{1}{2}=2\sqrt{x}\)

Answer 1

\(b,x-\frac{1}{2}=2\sqrt{x}\)

\(\Leftrightarrow x-2\sqrt{x}-\frac{1}{2}=0\)

\(\Leftrightarrow\left(\sqrt{x}-1\right)^2-\frac{3}{2}=0\)

\(\Leftrightarrow\left(\sqrt{x}-1-\sqrt{\frac{3}{2}}\right)\left(\sqrt{x}-1+\sqrt{\frac{3}{2}}\right)=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{5+2\sqrt{6}}{2}\\x=\frac{5-2\sqrt{6}}{2}\end{matrix}\right.\)