Question:
If \[ a+b=8 \quad \text{and} \quad ab=6 \] find:
\[ a^3+b^3 \]
Solution:
Using identity:
\[ a^3+b^3=(a+b)^3-3ab(a+b) \]
Substituting the given values:
\[ a^3+b^3=(8)^3-3(6)(8) \]
\[ =512-144 \]
\[ =368 \]
If \[ a+b=8 \quad \text{and} \quad ab=6 \] find:
\[ a^3+b^3 \]
Using identity:
\[ a^3+b^3=(a+b)^3-3ab(a+b) \]
Substituting the given values:
\[ a^3+b^3=(8)^3-3(6)(8) \]
\[ =512-144 \]
\[ =368 \]