Question:
If $a+b=10$ and $a b=21$, Find the value of $a^{3}+b^{3}$
Solution:
Given,
$a+b=10, a b=21$
we know that, $(a+b)^{3}=a^{3}+b^{3}+3 a b(a+b) \quad \ldots 1$
substitute $a+b=10, a b=21$ in eq 1
$\Rightarrow(10)^{3}=a^{3}+b^{3}+3(21)(10)$
$\Rightarrow 1000=a^{3}+b^{3}+630$
$\Rightarrow 1000-630=a^{3}+b^{3}$
$\Rightarrow 370=a^{3}+b^{3}$
Hence, the value of $a^{3}+b^{3}=370$
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