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\ 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(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 ,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 (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 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

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

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

If a ,\ b ,\ c ,\ d are in G.P., show that: (a b+b c+c d)^2=(a^2+b^2+c^2)(b^2+c^2+d^2)

If a,b,c,d………are in G.P., then show that (a+b)^2, (b+c)^2, (c+d)^2 are in G.P.

If a,b,c,d………are in G.P., then show that (a-b)^2, (b-c)^2, (c-d)^2 are in G.P.