Question

If p² + q² - r² = 0, then the value of (p⁶ + q⁶ - r⁶) ÷ p²q²r² is:

1. -3
2. 1/3
3. 3
4. 3pqr

Answer 1

Correct Answer - Option 1 : -3

Given:

p2 + q2 - r2 = 0

Formula used:

(a + b)³ = a³ + b³ + 3ab(a + b)

Calculation:

Given that, p2 + q2 - r2 = 0

⇒ p2 + q2 = r2

By cubing both sides.

⇒ (p2 + q2)³ = r⁶

⇒ p⁶ + q⁶ + 3. p².q²(p2 + q2) = r⁶

⇒ p6 + q6 + 3. p2.q2.r² = r⁶      ∵   [p2 + q2 = r2] 

⇒  p6 + q6 - r6 = - 3p2q2r2

∴ (p6 + q6 - r6) ÷ p2q2r2 = - 3