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-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)-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

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 |[b c-a^2,a c-b^2,a b-c^2],[a c-b^2,a b-c^2,b c-a^2],[a b-c^2,b c-a^2,a c-b^2]| is a. always positive b. always negative c. always zero d. cannot say anything

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

Show that the determinant |a^2+b^2+c^2b c+c a+a bb c+c a+a bb c+c a+a b a^2+b^c+c^2b c+c a+a bb c+c a+a bb c+c a+a b a^2+b^2+c^2| is always non-negative. When is the determinant zero?

Show that the determinant |a^2+b^2+c^2b c+c a+a bb c+c a+a bb c+c a+a b a^2+b^c+c^2b c+c a+a bb c+c a+a bb c+c a+a b a^2+b^2+c^2| is always non-negative. When is the determinant zero?

If a ,b ,c ,da n dp are distinct real numbers such that (a^2+b^2+c^2)p^2-2(a b+b c+c d)p+(b^2+c^2+d^2)lt=0, then prove that a ,b ,c , d are in G.P.