Answer to Question #29822 in Algebra for adrian thomas

Question

If a,b,c,d and p re distinct real numbers such that (a^2+b^2+c^2)p^2-2p(ab+bc+cd)+(b^2+c^2+d^2)≤0 then a,b,c,d are in A.P/ G.P/ H.P/ab=cd