Question:
If $a+b=8$ and $a b=6$, find the value of $a^{3}+b^{3}$
Solution:
Given,
a + b = 8 and ab = 6
We know that,
$a^{3}+b^{3}=(a+b)^{3}-3 a b(a+b)$
$\Rightarrow a^{3}+b^{3}=(a+b)^{3}-3 a b(a+b)$
$\Rightarrow a^{3}+b^{3}=(8)^{3}-3(6)(8)$
$\Rightarrow a^{3}+b^{3}=512-144$
$\Rightarrow a^{3}+b^{3}=368$
Hence, the value of $a^{3}+b^{3}$ is 368
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