\(2a^2+2b^2=5ab\\ \Leftrightarrow2a^2-5ab+2b^2=0\\ \Leftrightarrow2a^2-4ab-ab+2b^2=0\\ \Leftrightarrow2a\left(a-2b\right)+b\left(a-2b\right)=0\\ \Leftrightarrow\left(2a+b\right)\left(a-2b\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}a=-\dfrac{b}{2}\\a=2b\end{matrix}\right.\)
Với \(a=-\dfrac{b}{2}\Leftrightarrow Q=\dfrac{-\dfrac{b}{2}+b}{-\dfrac{b}{2}-b}=\dfrac{b}{2}:\dfrac{-3b}{2}=\dfrac{b}{-3b}=-\dfrac{1}{3}\)
Với \(a=2b\Leftrightarrow Q=\dfrac{3b}{b}=3\)
\(2a^2+2b^2=5ab\)
\(\Leftrightarrow\left(2a^2-4ab\right)+\left(2b^2-ab\right)=0\)
\(\Leftrightarrow2a\left(a-2b\right)-b\left(a-2b\right)=0\)
\(\Leftrightarrow\left(a-2b\right)\left(2a-b\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=2b\\b=2a\end{matrix}\right.\)
TH1: a=2b
\(Q=\dfrac{a+b}{a-b}=\dfrac{2b+b}{2b-b}=\dfrac{3b}{b}=3\)
TH2: b=2a
\(Q=\dfrac{a+b}{a-b}=\dfrac{a+2a}{a-2a}=\dfrac{3a}{-a}=-3\)
