Question 87

If $$a^{3} - b^{3}$$ = 91 and a - b = 1, then what is the value of ab?

Solution

Given : $$a^{3} - b^{3}$$ = 91 -----------(i)

Also, $$a-b=1$$ -----------(ii)

Cubing both sides, we get :

=> $$(a-b)^3=(1)^3$$

=> $$a^3-b^3-3ab(a-b)=1$$

Substituting values from equation (i) and (ii)

=> $$91-3ab(1)=1$$

=> $$3ab=91-1=90$$

=> $$ab=\frac{90}{3}=30$$

=> Ans - (D)

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