If $$a^3 - b^3 = 208 and a - b = 4, then (a + b )^2 - ab$$ is equal to:
From the given question,
$$a^3 - b^3 = 208$$ and $$a - b = 4$$
$$(a-b)^3=a^3-b^3-3ab(a-b)$$
Substituting the values,
$$\Rightarrow 4^3=208-3ab(4)$$
$$\Rightarrow ab=\dfrac{208-64}{12}=\dfrac{144}{12}=12$$
Now, $$(a+b)^2=(a-b)^2+4ab$$
$$\Rightarrow (a+b)^2-ab=(a-b)^2+3ab=4^2+3\times 12$$
$$\Rightarrow (a+b)^2-ab=52$$
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