Question

Giải phương trình: \(x^2-2\sqrt{2x-1}=\frac{13x^2-28x+24}{2x+1}\)

Answer 1

ĐKXĐ: \(x\ge\frac{1}{2}\)

\(\Leftrightarrow x^2-x-1-\frac{13x^2-28x+24}{2x+1}+x+1-2\sqrt{2x-1}=0\)

\(\Leftrightarrow\frac{2x^3-14x^2+25x-25}{2x+1}+\frac{\left(x+1\right)^2-4\left(2x-1\right)}{x+1+2\sqrt{2x-1}}=0\)

\(\Leftrightarrow\frac{\left(x-5\right)\left(2x^2-4x+5\right)}{2x+1}+\frac{\left(x-1\right)\left(x-5\right)}{x+1+2\sqrt{2x-1}}=0\)

\(\Leftrightarrow\left(x-5\right)\left(\frac{2x^2-4x+5}{2x+1}+\frac{x-1}{x+1+2\sqrt{2x-1}}\right)=0\)

\(\Rightarrow x=5\) (ngoặc to luôn dương với \(x\ge\frac{1}{2}\))