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Question

If a,b,c are real numbers, then a(ab)+b(bc)+c(ca)=0, only if

A
a+b+c=0
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B
a=b=c
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C
Either a=b or b=c or c=a
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D
abc=0
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Solution

The correct option is B a=b=c
a(ab)+b(bc)+c(ca)=0
a2+b2+c2abbcca=0
2a2+2b2+2c22ab2bc2ca=0
(ab)2+(bc)2+(ca)2=0
ab=0 and bc=0 and ca=0
a=b=c

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