if-a-b-c-0-find-the-value-of-a-2-bc-b-2-ca-c-2-ab-

Question Number 171826 by Mikenice last updated on 21/Jun/22

i f a + b + c = 0, f i n d t h e v a l u e o f

\frac{a^{2}}{b c} + \frac{b^{2}}{c a} + \frac{c^{2}}{a b}

Answered by nimnim last updated on 21/Jun/22

\frac{a^{2}}{b c} + \frac{b^{2}}{c a} + \frac{c^{2}}{a b}

= \frac{a^{3} + b^{3} + c^{3}}{a b c}

= \frac{a^{3} + b^{3} + c^{3}}{a b c} - 3 + 3

= \frac{a^{3} + b^{3} + c^{3} - 3 a b c}{a b c} + 3

= \frac{(a + b + c) (a^{2} + b^{2} + c^{2} - a b - b c - c a)}{a b c} + 3

= \frac{(0) (a^{2} + b^{2} + c^{2} - a b - b c - c a)}{a b c} + 3

= 0 + 3

= 3

Commented by Mikenice last updated on 21/Jun/22

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