Question : If $p^{3}+3p^{2}+3p=7$, then the value of $p^2+2p$ is:
Option 1: 4
Option 2: 3
Option 3: 5
Option 4: 6
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Correct Answer: 3
Solution :
Given that:
$p^3 + 3p^2 + 3p = 7$
Adding unity to both sides,
$p^3 + 3p^2 + 3p + 1 = 7 + 1$
⇒ $(p+1)^3 = (2)^3$
⇒ $p+1=2$
⇒ $p = 1$
$\therefore p^2 + 2p = 1 + 2 \times 1 = 3$
Hence, the correct answer is 3.
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