Question

if a,b,c are all non zero and a+b+c=0,prove that a square + b square +c square upon ab +bc +ca=3

Answer 1

a+b+c=0
⇒(a+b+c)²=a²+b²+c²+2(ab+bc+ca) 
Since a+b+c=0 , (a+b+c)²=0
⇒a²+b²+c²+2(ab+bc+ca)=0
⇒a²+b²+c²=-2(ab+bc+ca)
⇒$\frac{a^{2}+b^{2}+c^{2} }{ab+bc+ca}$ = -2
Ans:$\frac{a^{2}+b^{2}+c^{2} }{ab+bc+ca}$ = -2
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