Question 87

If a + b = 5 and ab = 6, then what is the value of $$a^{3} + b^{3}$$ ?

Solution

Given :  $$ab=6$$ -----------(i)

Also, $$a+b=5$$ -----------(ii)

Cubing both sides, we get :

=> $$(a+b)^3=(5)^3$$

=> $$a^3+b^3+3ab(a+b)=125$$

Substituting values from equation (i) and (ii)

=> $$a^3+b^3+3(6)(5)=125$$

=> $$a^3+b^3=125-90=35$$

=> Ans - (C)