\(y^2+2xy+4=2x+5y\)
\(\Leftrightarrow y^2+\left(2x-5\right)y-2x+4=0\)
\(a+b+c=1+2x-5-2x+4=0\)
\(\Rightarrow\left[{}\begin{matrix}y=1\\y=-2x+4\end{matrix}\right.\)
- Với \(y=1\Rightarrow5x^2-11=\sqrt{x^4+4}\) (\(x\ge\sqrt{\frac{11}{5}}\))
\(\Leftrightarrow\left(5x^2-11\right)^2=x^4+4\)
\(\Leftrightarrow24x^4-110x^2+117=0\Leftrightarrow...\)
- Với \(y=-2x+4\)
\(5x^2-14x+10=\sqrt{x^4+4}=\sqrt{x^4+4x^2+4-\left(2x\right)^2}\)
\(\Leftrightarrow5x^2-14x+10=\sqrt{\left(x^2-2x+2\right)\left(x^2+2x+2\right)}\)
Đặt \(\left\{{}\begin{matrix}\sqrt{x^2-2x+2}=a>0\\\sqrt{x^2+2x+2}=b>0\end{matrix}\right.\)
\(\Rightarrow6a^2-b^2=ab\Leftrightarrow6a^2-ab-b^2=0\)
\(\Leftrightarrow\left(3a+b\right)\left(2a-b\right)=0\Rightarrow b=2a\)
\(\Rightarrow\sqrt{x^2+2x+2}=2\sqrt{x^2-2x+2}\)
\(\Leftrightarrow x^2+2x+2=4\left(x^2-2x+2\right)\)
\(\Leftrightarrow...\)
