ABC26GN1209 · Simplification

$$\begin{aligned} x+y=1 & \Rightarrow(x+y)^{2}=1^{2}=1 \Rightarrow x^{2}+y^{2}+2 x y=1 \\ & \Rightarrow x^{2}+y^{2}=1-2 x y \\ & \Rightarrow\left(x^{2}+y^{2}\right)^{2}=(1-2 x y)^{2} \\ & \Rightarrow x^{4}+y^{4}+2 x^{2} y^{2}=1+4 x^{2} y^{2}-4 x y \\ & \Rightarrow 2 x^{2} y^{2}-4 x y=17-1=16 \quad\left[\because x^{4}+y^{4}=17\right] \\ & \Rightarrow x^{2} y^{2}-2 x y=8 . \end{aligned}$$