Question

QUESTION :-
Given :- a+b+c= 0
then find value of a²/bc + b²/ca + c²/ab
please explain the answer step by step​

Answer 1

Answer:

b) 0

100% correct

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Answer 2

Explanation:

$\mathsf{\therefore\dfrac{a^{2}}{bc}+\dfrac{b^{2}}{ca}+\dfrac{c^{2}}{ab}}$

$\mathsf{=\dfrac{a^{2}\times a+b^{2}\times b+c^{2}\times c}{abc}}$

$\mathsf{=\dfrac{a^{3}+b^{3}+c^{3}}{abc}}$

$\mathsf{=\dfrac{(a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca)+3abc}{abc}}$

since

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

$\mathsf{=\dfrac{0\times (a^{2}+b^{2}+c^{2}-ab-bc-ca)+3abc}{abc}}$

since $\mathsf{a+b+c=0}$

$\mathsf{=\dfrac{0+3abc}{abc}}$

$\mathsf{=\dfrac{3abc}{abc}}$

$\mathsf{=3}$

Option (d) 3 is correct.