if a^2+b^2+c^2-ab-bc-ca = 0 ,prove that a=b=c

Answers (1)

SOLUTION:     We have,

               a^2+b^2+c^2-ab-bc-ca = 0

        [ multiplying both side by 2 ]

      we gate , 2a^2+2b^2+2c^2-2ab-2bc-2ca = 0

                     left ( a^2-2ab+b^2 
ight ) +(b^2-2bc+c^2) +(c^2-2ac+a^2) = 0

                    left ( a-b 
ight )^2+(b-c)^2 + (c-a)^2 = 0

                  	herefore a-b =0 , b-c = 0 , c-a = 0

                   a=b, b=c , c=a    Rightarrow a=b=c

                  

                   

           

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