If `a ,\ b ,\ c ,\ d\ a n d\ p` are different real numbers such that: `(a^2+b^2+c^2)p^(I2)-2(a b+b c+c d)p+(b^2+c^2+d^2)lt=0` , then show that `a ,\ b ,\ c` and `d` are in G.P.

If a,b,c,d and p are different real numbers such that: (a^(2)+b^(2)+c^(2))p^(I2)-2(ab+bc+cd)p+(b^(2)+c^(2)+d^(2))<=0 ,then show that a,b,c and d are in G.P.

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))<=0 ,then show that a,b,c and d are in G.P.

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

if a,b, c, d and p are distinct real number such that (a^(2) + b^(2) + c^(2))p^(2) - 2p (ab + bc + cd) + (b^(2) + c^(2) + d^(2)) lt 0 then a, b, c, d are in

Let a,b,c,d and p be any non zero distinct real numbers such that (a^(2) + b^(2) + c^(2))p^(2) - 2(ab+bc+cd)p+ (b^(2) + c^(2) + d^(2))=0 . Then :

If a,b,c,d and p are distinct real numbers such that (1987,2M)(a^(2)+b^(2)+c^(2))p^(2)-2(ab+bc+cd)P+(b^(2)+c^(2)+d^(2))>=0, then a,b,c,d are in AP(b) are in GP are in HP(d) satisfy ab=cd

If a,b,c,d are such unequal real numbers that (a^(2)+b^(2)+c^(2))p^(2)-2 (ab+bc+cd) p+ (b^(2)+c^(2)+d^(2)) le 0 then a,b,c, d are in -

If a,b,c are distinct real numbers such that a, b,c are in A.P.and a^(2),b^(2),c^(2) are in H.P, then

a,b,c,d are four different real numbers which are in APIf 2(a-b)+x(b-c)^(2)+(c-a)^(3)=2(a-d)+(b-d)^(2)+(c-d)^(3), then