Question 71

If $$a^3 - b^3 = 2349$$ and $$(a - b) = 9$$, then $$(a + b)^2 - ab$$ is equal to:

Solution

$$(a-b)=9$$.............(1)

$$(a-b)^3=729$$

$$a^3-b^3-3ab\left(a-b\right)=729$$

$$2349-3ab\left(9\right)=729$$

$$27ab=1620$$

$$ab=60$$..............(2)

$$(a-b)=9$$

$$(a-b)^2=81$$

$$a^2+b^2-2ab=81$$

$$a^2+b^2-2\left(60\right)=81$$

$$a^2+b^2-120=81$$

$$a^2+b^2=201$$..........(3)

$$(a+b)^2-ab=a^2+b^2+2ab-ab$$

$$=a^2+b^2+ab$$

$$=201+60$$

$$=261$$

Hence, the correct answer is Option C

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