Question
Download Solution PDFIf a3 + 3a2 + 3a = 63, then the value of a2 + 2a is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
Let's solve the given equation \(a^3 + 3a^2 + 3a = 63\) and find the value of \(a^2 + 2a\)
We can factor the left side of the equation by recognizing it as a cube of a binomial:
\((a + 1)^3 = a^3 + 3a^2 + 3a + 1 \)
Comparing this with the given equation, we have:
\((a + 1)^3 = 63 + 1\)
Taking the cube root of both sides, we get:
a + 1 = ∛(64)
Simplifying further, we have:
a + 1 = 4
Subtracting 1 from both sides:
a = 4 - 1
a = 3
Now we can find the value of \(a^2 + 2a:\)
\(a^2 + 2a = 3^2 + 2(3) = 9 + 6 = 15\)
Therefore, the value of \(a^2 + 2a\) is 15.
∴ Option 3 is the correct answer.
Last updated on Jul 21, 2025
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