" 33.If "a^(2)+b^(2)+c^(2)-ab-bc-ca=0," prove that "a=b=c

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

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

If a^2 + b^2 + c^2 - ab - bc - ca = 0 , then prove that a=b=c.

Prove that a^(2)+b^(2)+c^(2)-ab-bc-ca is always non-negative for all values of a,b and c.

Prove that a^(2)+b^(2)+c^(2)-ab-bc-ca is always non-negative for all values of a,b and c

If a^(2)(b+c),b^(2)(c+a),c^(2)(a+b) are in A.P. then prove that a,b,c are in A.P.or ab+bc+ca=0

Given : a^(2)+b^(2)+c^(2) =0 Prove the following : |{:(b^(2)+c^(2),ab,ca),(ab,c^(2)+a^(2),bc),(ca,bc,a^(2)+b^(2)):}|=4a^(2)b^(2)c^(2)

If a,b,c are all non-zero and a+b+c=0, prove that a^2/(bc)+b^2/(ca)+c^2/(ab)=3 .