If a + b + c = 0, Then Find the Value of a³ + b³ + c³
Question:
If \(a + b + c = 0\), then write the value of \(a^3 + b^3 + c^3\).
Solution
We know that
\[ a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca) \]
Given:
\[ a+b+c=0 \]
Putting the value in identity:
\[ a^3+b^3+c^3-3abc=0 \]
\[ a^3+b^3+c^3=3abc \]
Therefore,
\[ \boxed{a^3+b^3+c^3=3abc} \]