If a2 + b2 = 5ab, then the value of ( a^2b^2 + b^2a^2 ) is?

Answer: Option C

$$\begin{array}{rl}& a^2+b^2=5ab\\ & \Rightarrow \frac{a^2}{ab}+\frac{b^2}{ab}=5\\ & \Rightarrow \frac{a}{b}\text{ + }\frac{b}{a}\text{ = 5}\\ & \text{Squaring the both sides}\\ & \Rightarrow {\left(\frac{a}{b}\right)}^2\text{ + }{\left(\frac{b}{a}\right)}^2+2\times \frac{a}{b}\times \frac{b}{a}=25\\ & \Rightarrow \frac{a^2}{b^2}\text{ + }\frac{b^2}{a^2}=25-2\\ & \Rightarrow \frac{a^2}{b^2}\text{ + }\frac{b^2}{a^2}=23\end{array}$$