If x + y = √3 and x - y = √2, then the value of 8xy(x2 + y2) is?

Answer: Option C

$$\begin{array}{rl}& x+y=\sqrt{3}.......\text{(i)}\\ & x-y=\sqrt{2}.......(ii)\\ & \text{From equation (i) and (ii)}\\ & x=\frac{\sqrt{3}+\sqrt{2}}{2}\\ & y=\frac{\sqrt{3}-\sqrt{2}}{2}\\ & \text{So, }8xy\left(x^2+y^2\right)\\ & =8\times \frac{\sqrt{3}+\sqrt{2}}{2}\times \frac{\sqrt{3}-\sqrt{2}}{2}\left[\frac{{\left(\sqrt{3}+\sqrt{2}\right)}^2}{4}+\frac{{\left(\sqrt{3}-\sqrt{2}\right)}^2}{4}\right]\\ & =2\left(3-2\right)\left[\frac{3+2+2\sqrt{6}+3+2-2\sqrt{6}}{4}\right]\\ & =2\times 1\times \frac{10}{4}\\ & =5\end{array}$$