Question

Giải phương trình : 25x + 2y\(^2\) - 10\(\sqrt{x}\)y - 10\(\sqrt{x}\) +2 =0

Answer 1

Lời giải:

Ta có: \(25x+2y^2-10\sqrt{x}y-10\sqrt{x}+2=0\)

\(\Leftrightarrow [(5\sqrt{x})^2+y^2-10\sqrt{x}y]+y^2-10\sqrt{x}+2=0\)

\(\Leftrightarrow (5\sqrt{x}-y)^2+y^2-10\sqrt{x}+2=0\)

\(\Leftrightarrow (5\sqrt{x}-y)^2-2(5\sqrt{x}-y)+1-2y+y^2+1=0\)

\(\Leftrightarrow (5\sqrt{x}-y-1)^2+(y-1)^2=0\)

Do đó: \(\left\{\begin{matrix} 5\sqrt{x}-y-1=0\\ y-1=0\end{matrix}\right.\Rightarrow \left\{\begin{matrix} y=1\\ x=\frac{4}{25}\end{matrix}\right.\)