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,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 different 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 show that a, b, c and 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^2-2(ab+bc+cd)p+(b^2+c^2+d^2)le0 then a,b,c,d are in

If a ,\ b ,\ c ,\ d\ a n d\ p are different 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 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+b c+cd) p +(b^2+c^2+d^2) le 0 , then show that a, b, c and d are in G.P .

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 ,d and p are distinct real numbers such that (1987, 2M) (a^2+b^2+c^2)p^2-2(a b+b c+c d)P+(b^2+c^2+d^2)geq0,t h e na , b , c , d are in AP (b) are in GP are in HP (d) satisfy a b=c d

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 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) le 0 , then show that a, b, c and d are in GP.