Question 78

What is the value of equation $$a^3 + b^3 + c^3 - 3abc$$ if $$a^2 + b^2 + c^2 = ab + bc + ca + 4$$ and $$a + b + c = 4$$

Solution

Given : $$a + b + c = 4$$ -----------(i)

and $$a^2 + b^2 + c^2 = ab + bc + ca + 4$$

=> $$a^2 + b^2 + c^2 - ab - bc - ca = 4$$ ------------(ii)

To find : $$a^3 + b^3 + c^3 - 3abc$$

= $$(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$$

Substituting values from equations (i) and (ii), we get :

= $$4\times4=16$$

=> Ans - (C)

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