Question : If $a+b=8$ and $ab=15$, then $(a^3+b^3)$ is equal to:
Option 1: 224
Option 2: 244
Option 3: 152
Option 4: 128
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Correct Answer: 152
Solution :
Given: $a+b=8$ and $ab=15$
We know the algebraic identity, $(a^{3}+b^{3})=(a+b)^3-3ab(a+b)$.
By substituting the values in the above equation, we get,
$⇒(a^{3}+b^{3})=8^3-3×15×8$
$\therefore (a^{3}+b^{3})=152$
Hence, the correct answer is 152.
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