Given a x^2+b x+c 0, b x^2+c x+a and c x^2+a x+b 0 , where a b c and a, b, c R . Now a^2+b^2+c^2 a b+b c+c a can not take values

Step-by-step solution

Given a b c, a, b, c R Now a x^2+b x+c 0 b^2-4 a c 0 and a 0b x^2+c x+a 0 c^2-4 a b 0 and b 0c x^2+a x+b 0 a^2-4 b c 0 and c 0 Equality can not hold simultancously ( a b c) a ^2+ b ^2+ c ^2 ab + bc + ca 4 and since a b c aligned & (a-b)^2+(b-c)^2+(c-a)^2 0 & a^2+b^2+c^2 a b+b c+c a 1 & a^2+b^2+c^2 a b+b c+c a (1.4) aligned