Question

If $p,q,r$ be three distinct real numbers in A.P. then $p^3+r^3$ equals

• A. $pqr$
• B. $-3pqr$
• C. $-6pqr$
• D. none of these

Answer 1

Answer: (D)

none of these

Given:

$p,q,r$ are in A.P.

$\therefore 2q=p+r$

Cubing both sides:

$\Rightarrow p^3+r^3+3p^{2}r+3p{r}^2=8q^3$

$\therefore p^3+r^3=8q^3-3p^{2}r-3p{r}^2$