Question

Giải phương trình: \(15x-2x^2-5=\sqrt{2x^2-15x+11}\)

Answer 1

\(-2x^2+15x-5=\sqrt{2x^2-15x+11}\)

\(pt\Leftrightarrow-2x^2+15x-7=\sqrt{2x^2-15x+11}-2\)

\(\Leftrightarrow-\left(x-7\right)\left(2x-1\right)=\dfrac{2x^2-15x+11-4}{\sqrt{2x^2-15x+11}+2}\)

\(\Leftrightarrow-\left(x-7\right)\left(2x-1\right)-\dfrac{\left(x-7\right)\left(2x-1\right)}{\sqrt{2x^2-15x+11}+2}=0\)

\(\Leftrightarrow-\left(x-7\right)\left(2x-1\right)\left(1+\dfrac{1}{\sqrt{2x^2-15x+11}+2}\right)=0\)

Dễ thấy:\(1+\dfrac{1}{\sqrt{2x^2-15x+11}+2}>0\)

\(\Rightarrow\left[{}\begin{matrix}x-7=0\\2x-1=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=7\\x=\dfrac{1}{2}\end{matrix}\right.\)