Correct Answer: 5

Solution : According to the question,
x + y = √3
Squaring both sides, we get,
⇒ x ² + y ² + 2xy = 3 ––––––––––––(i)
Now, x – y = √2
Squaring both sides, we get,
⇒ x ² + y ² – 2xy = 2 ––––––––––––(ii)
Adding equations (i) and (ii), we get,
2x ² + 2y ² = 5
⇒ x ² + y ² = $\frac{5}{2}$ ––––––––––––––––(iii)
Now putting the value from equation (iii) in equation (i), we get,
$\frac{5}{2}$ + 2xy = 3
⇒ 2xy = 3 – $\frac{5}{2}$
⇒ 2xy = $\frac{1}{2}$
$\therefore$ xy = $\frac{1}{4}$
Now, the value of 8xy(x ² + y ² )
= $8 × \frac{1}{4} × \frac{5}{2}$
= $5$
Hence, the correct answer is 5.