If a³ + 3a² + 3a = 7, then find the value of a² + 2a.

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Accepted Answer

Given: a³ + 3a² + 3a = 7

Recall the expansion of (a + 1)³ = a³ + 3a² + 3a + 1.

From the given equation, a³ + 3a² + 3a = 7.
Add 1 to both sides:
(a³ + 3a² + 3a) + 1 = 7 + 1
=> (a + 1)³ = 8

Taking cube root on both sides:
=> a + 1 = 2
=> a = 1

Now, find a² + 2a:
= (1)² + 2(1) = 1 + 2 = 3

Therefore, the value of a² + 2a is 3.

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