NIELIT 2022 Feb Scientist C - Section D: 26

Question

If $p^{3} + 3p^{2} + 3p = 7,$ then the value of $p^{2} + 2p$ is :

• A. $1$
• B. $3$
• C. $5$
• D. $15$

Answer 1

Given that: $p^3+3p^2+3p=7$,put $p=1$ we will get LHS=RHS,for $p=1$ given equation satisfied.

so the value of $p^2+2p=1+2=3$

Option (B) is correct.

Answer 2

(p+1)^3 = p^3 + 1 + 3p(p+1)

              =[p^3+3p^2+3p] + 1

              =7+1=8

therefore p+1=2 => p=1

so answer is 3