cho ab(x²+y²)+xy(a²+b²)=ab.trong đó x,y khác 0,x+y=1.CMR:a=b Giúp mjnhf vs mính cần gấpp ạ

$\begin{array}{l} ab\left( {{x^2} + {y^2}} \right) + xy\left( {{a^2} + {b^2}} \right) = ab\\  \Leftrightarrow ab\left[ {{{\left( {x + y} \right)}^2} – 2xy} \right] + xy\left( {{a^2} + {b^2}} \right) = ab\\  \Leftrightarrow ab{\left( {x + y} \right)^2} – 2xyab + xy\left( {{a^2} + {b^2}} \right) = ab\\  \Leftrightarrow ab + xy\left( {{a^2} + {b^2} – 2ab} \right) = ab\\  \Leftrightarrow xy{\left( {a – b} \right)^2} = 0\\  \Leftrightarrow a = b\left( {x,y \ne 0} \right) \end{array}$