Question 63

If a-b=1 and $$a^{3}-b^{3}$$ = 61, then the value of ab will be

Solution

Given : $$(a-b)=1$$ and $$(a^3-b^3)=61$$

We know that, $$(a^3-b^3)=(a-b)(a^2+b^2+ab)$$

=> $$61=1(a^2+b^2+ab)$$

=> $$a^2+^2+ab=61$$

=> $$a^2+b^2=61-ab$$ ----------(i)

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

Substituting value from equation (i)

=> $$(1)^2=(61-ab)-2ab$$

=> $$1=61-3ab$$

=> $$3ab=61-1=60$$

=> $$ab=\frac{60}{3}=20$$

=> Ans - (B)

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