Prove that `a^2+b^2+c^2-a b-b c-c a` is always non-negative for all values of `a ,ba n dcdot`

Prove that a^2+b^2+c^2-a b-b c-c a is always non-negative for all values of a ,b a nd c.

Prove that a^2+b^2+c^2-a b-b c-c a is always non-negative for all values of a ,\ b\ a n d\ 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

Given that a ,b ,c are distinct real numbers such that expressions a x^2+b x+c ,b x^2+c x+aa n dc x^2+a x+b are always non-negative. Prove that the quantity (a^2+b^2+c^2)//(a b+b c+c a) can never lie inn (-oo,1) uu [4 , oo) .

Given that a ,b ,c are distinct real numbers such that expressions a x^2+b x+c ,b x^2+c x+aa n dc x^2+a x+b are always non-negative. Prove that the quantity (a^2+b^2+c^2)//(a b+b c+c a) can never lie inn (-oo,1) uu [4 , oo) .

Given that a ,b ,c are distinct real numbers such that expressions a x^2+b x+c ,b x^2+c x+a and,c x^2+a x+b are always non-negative. Prove that the quantity (a^2+b^2+c^2)/(a b+b c+c a) can never lie in (-oo,1) uu [4 , oo) .

The value of determinant |b c-a^2a c-b^2a b-c^2a c-b^2a b-c^2b c-a^2a b-c^2b c-a^2a c-b^2| is a. always positive b. always negative c. always zero d. cannot say anything

The value of determinant |b c-a^2a c-b^2a b-c^2a c-b^2a b-c^2b c-a^2a b-c^2b c-a^2a c-b^2| is a. always positive b. always negative c. always zero d. cannot say anything

The value of determinant |(bc-a^(2),ac-b^(2),ab-c^(2)),(ac-b^(2),ab-c^(2),bc-a^(2)),(ab-c^(2),bc-a^(2),ac-b^(2))| is a)always non -negative b)always non-positive c)always zero d)can't say anything