If a, b, c, d and p are distinct real numbers such that (a^2+b^2+c^2 ) p^2-2 p(a b+b c+c d)+ (b^2+ . .c^2+d^2 ) 0 , then

Step-by-step solution

The given relation can be written as (a^2 p^2-2 a b p+b^2 )+ (b^2 p^2+c^2-2 b p c )+ (c^2 p^2+d^2-2 p c d ) 0 or (a p-b)^2+(b p-c)^2+(c p-d)^2 0 ...(1) Since a, b, c , d and p are all real, the inequality (1) is possible only when each of factor is zero. i.e., a p-b=0, b p-c=0 and c p-d=0 or p= b a = c b = d c or a, b, c, d are in G.P.