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NIMCET 2020 Official Paper

Option 3 : 3

NIMCET 2020 Official Paper

1447

120 Questions
480 Marks
120 Mins

__Concept:__

- (a + b + c)(a
^{2}+ b^{2}+ c^{2}- ab - bc - ca) = a^{3}+ b^{3}+ c^{3}- 3abc. - If a + b + c = 0, then a
^{3}+ b^{3}+ c^{3}= 3abc.

**Calculation:**

Since, a + b + c = 0, we have a^{3} + b^{3} + c^{3} = 3abc.

∴ The given expression is:

\(\rm \dfrac{a^2}{bc} + \dfrac{b^2}{ca} + \dfrac{c^2}{ab}\)

= \(\rm \dfrac{a^3}{abc} + \dfrac{b^3}{bca} + \dfrac{c^3}{cab}\)

= \(\rm \dfrac{3abc}{abc}\) = **3**.