If a, b, c, d and p are different real numbers such that `(a^2 + b^2 + c^2)p^2 – 2(ab + bc + cd) p + (b^2 + c^2 + d^2) le 0` , then show that a, b, c and d are in GP.

If a, b, d and p are distinct non - zero real numbers such that (a^2+b^2 + c^2) p^2 - 2(ab+bc+cd)p+(b^2 + c^2 +d^2) le 0 then n. Prove that a, b, c, d are in G. P and ad = bc

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.

If (a+bx)/(a-bx)=(b-cx)/(b-cx)=(c+dx)/(c-dx)( x ne 0) then show that a, b, c and d are in G.P.

If a, b, c, d are distinct integers in A. P. Such that d=a^2+b^2+c^2 , then a + b + c + d is

If a, b, c and d are in G.P. show that (a^2+b^2+c^2)(b^2+c^2+d^2) = (ab+bc+cd)^2

If a, b, c, d are in G.P, prove that (a^n + b^n), (b^n + c^n), (c^n + d^n) are in G.P.

If a,b , c are distinct +ve real numbers and a^(2)+b^(2)+c^(2)=1" then "ab+bc+ca is

If a , b ,c are three distinct positive real numbers in G.P., then prove that c^2+2a b >3a cdot

If a,b, and c are in G.P then a+b,2b and b+ c are in

If a,b,c,d are in a geometric sequences, then show that (a-b+c) (b+c+d) = ab + bc + cd.