Question 58

If a + b + c = 10 and ab + bc + ca = 32 then $$a^3 + b^3 + c^3 - 3abc$$ is equal to:

Solution

$$a^3 + b^3 + c^3 - 3abc = (a + b +c)(a^2 + b^2 + c^2 -ab -bc -ca)$$

First calculate $$a^2 + b^2 + c^2$$,

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

$$ a^2 + b^2 + c^2 = 100 - 64 = 36$$

Putting this value in equation 1 , we get ,

$$a^3 + b^3 + c^3 - 3abc = 10 (36 - 32) = 40$$

So , the answer would be option b)40.

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