If $$a^3 + b^3 = 110 and a + b = 5$$, then $$(a + b)^2 - 3ab$$ is equal to:
Given that,
$$a^3 + b^3 = 110$$ and a + b = 5
or $$(a+b)^2=25$$
$$\Rightarrow a^3 +b^3=(a+b)(a^2+b^2-ab)$$
$$\Rightarrow a^3 +b^3=(a+b)(a^2+b^2+2ab-2ab-ab)$$
$$\Rightarrow a^3 +b^3=(a+b)(a^2+b^2+2ab-3ab)$$
$$\Rightarrow a^3 +b^3=(a+b)((a+b)^2-3ab)$$
Now, substituting the values
$$\Rightarrow 110=5(25-3ab)$$
$$\Rightarrow 22=(25-3ab)$$
$$\Rightarrow 3ab=25-22 =3$$
So,
$$(a + b)^2 - 3ab= 25-3= 22$$
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