Question

cho (a+b+c)^2=3(ab+bc+ca) . Cm : a=b=c

Answer 1

Answer 2

\(\left(a+b+c\right)^2=3\left(ab+bc+ac\right)\)

=> a^2 + b^2 + c^2 +2ac+2bc+2ab = 3(ab+bc+ab)

=> a^2 + b^2 + c^2 = ac+ab+bc

=> a^2 + b^2 + c^2 -ac-ab-bc =0

=>a^2 - ac + b^2 -ab +c^2 -bc =0

=> a(a-c) + b(b-a) + c(c-b) = 0

=> a(a-c)=0 , b(b-a)=0 , c(c-b)=0

=> a=0 a-c=0 => a=c

b=0 b-a =0 => b=a

c=0 c-b=0=> c=b

=> a=b=c

Answer 3

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Answer 4

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