Question 37

If a + b = 4 and ab = 3, then what is the value of $$a^{3} + b^{3}$$ ?

Solution

Given : $$ab=3$$ -----------(i)

Also, $$a+b=4$$ -----------(ii)

Cubing both sides, we get :

=> $$(a+b)^3=(4)^3$$

=> $$a^3+b^3+3ab(a+b)=64$$

Substituting values from equation (i) and (ii)

=> $$a^3+b^3+3(3)(4)=64$$

=> $$a^3+b^3=64-36=28$$

=> Ans - (C)

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