If p3 + 3p2 + 3p = 26, then the value of p2 + 2p is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 8
Formula used:
(x + y)3 = x3 + y3 + 3xy(x + y)
Calculations:
⇒ p3 + 3p2 + 3p = 26
Adding 1 to both sides
⇒ p3 + 3p2 + 3p + 13 = 26 + 1
⇒ p3 + 13 + 3 × p × 1 × (p + 1) = 27
⇒ (p + 1)3 = 33
⇒ p + 1 = 3
⇒ p = 2
Hence, the value of p2 + 2p
⇒ 22 + 2 × 2 = 4 + 4 = 8