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2. Polynomials
easy
જો $a, b, c$ બધા શુન્યેતર હોય અને $a+b+c=0,$ તો સાબિત કરો કે $\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b}=3$
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
