Question

If (√7 + √5 - √3)(√7 + √5 + √3) = P + 2√Q, then, what is the value of √(P + Q + 5)?

1. 9
2. 7
3. 8
4. 6

Answer 1

Correct Answer - Option 2 : 7

(√7 + √5 - √3)(√7 + √5 + √3) = P + 2√Q

⇒ (√7 + √5)² – 3 = P + 2√Q

⇒ (7 + 5 + 2√35) – 3 = P + 2√Q

⇒ 9 + 2√35 = P + 2√Q

∴ P = 9 and Q = 35

According to question -

√(P + Q + 5) = √(9 + 35 + 5)

⇒ √49

⇒ 7