If a, b, c are all non-zero and a+b+c=0, prove that frac{a^{2}}{b c}+frac{b^{2}}{c a}+frac{c^{2}}{a

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2. Polynomials

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If $a, b, c$ are all non-zero and $a+b+c=0,$ prove that $\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b}=3$

Option A

Option B

Option C

Option D

Solution

We have $a, b, c$ are all non-zero and $a+b+c=0,$ therefore

$a^{3}+b^{3}+c^{3}=3 a b c$

Now, $\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b}=\frac{a^{3}+b^{3}+c^{3}}{a b c}=\frac{3 a b c}{a b c}=3$

Standard 9

Mathematics

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