If x + y = √3 and x – y = √2 , then the value

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

1. 6
2. √6
3. 5
4. √5

Correct Option: C

x + y = √3
x – y = √2
∴ (x + y)² + (x – y)² = 3 + 2
⇒ 2 (x² + y²) = 5 ...(i)
Again,
(x + y)² – (x – y)² = 3 – 2
⇒ 4xy = 1 ...(ii)
∴ (x² + y²) = 5 × 1 = 5