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B
b + c = a
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C
c + a = b
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D
a = b = c
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Solution
The correct option is D
a = b = c
a2+b2+c2−ab−bc−ca=02(a2+b2+c2−ab−bc−ca)=0(Multiplying by 2)⇒2a2+2b2+2c2−2ab−2bc−2ca=0⇒a2+b2−2ab+b2+c2−2bc+c2+a2−2ca=0⇒(a−b)2+(b−c)2+(c−a)2=0∴(a−b)2=0,then a−b=0⇒a=bSimilarly, (b−c)2=0, thenb−c=0⇒b=cand (c−a)2=0, then c−a=0⇒c=a∴a=b=c