Question 66

If $$a^3 - b^3 = 208 and a - b = 4, then (a + b )^2 - ab$$ is equal to:

Solution

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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