Question 37

If $$a^{3} + b^{3}$$ = 19 and a + b = 1, then what is the value of ab?

Solution

Given : $$a^{3} + b^{3}$$ = 19 -----------(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)

=> $$19+3ab(1)=1$$

=> $$3ab=1-19=-18$$

=> $$ab=\frac{-18}{3}=-6$$

=> Ans - (B)

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