The value of \(\frac{{(p - q)^3 + (q - r)^3 + (r - p)^3}}{{12(p - q)(q - r)(r - p)}}\), where p ≠ q ≠ r, is equal to:

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 09 Dec 2022 Shift 1)

Answer 1

Given:

\(\frac{{(p - q)^3 + (q - r)^3 + (r - p)^3}}{{12(p - q)(q - r)(r - p)}}\)

Formula used:

If p - q = a, q - r = b and r - p = c,

then a + b + c = 0

and a³+ b³ + c³ = 3abc

Calculation:

\(\frac{{(p - q)^3 + (q - r)^3 + (r - p)^3}}{{12(p - q)(q - r)(r - p)}}\)

⇒ \(3(p-q)(q-r)(r-p) \over 12(p-q)(q-r)(r-p)\)

⇒ \(3 \over 12\)

⇒ \(1 \over 4\)

∴ The value of he given expression is \(\bf 1 \over 4\).