Question:
If \( a + b + c = 2 \), \( a^2 + b^2 + c^2 = 36 \), then the value of \( a^3 + b^3 + c^3 - 3abc \) is:
If \( a + b + c = 2 \), \( a^2 + b^2 + c^2 = 36 \), then the value of \( a^3 + b^3 + c^3 - 3abc \) is:
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When solving for expressions like \( a^3 + b^3 + c^3 - 3abc \), use known algebraic identities and substitute the given values for quick simplification.
Updated On: Apr 17, 2025
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The Correct Option is B
Solution and Explanation
We use the identity for \( a^3 + b^3 + c^3 - 3abc \), which is given by:
\[
a^3 + b^3 + c^3 - 3abc = (a + b + c)\left( a^2 + b^2 + c^2 - ab - bc - ca \right)
\]
Substitute the known values into this identity and solve.
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