If three numbers a, b, c satisfy the relation `(a^2 + b^2)(b^2 + c^2) = (ab + bc)^2`, show that, a, b, c are in G.P.

Three numbers a,b,c are such that (a^(2) +ab+b ^(2))/(ab +bc +ca) =(a+b)/(a+c), then the numbers b, a, c are in-

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 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, 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, 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, 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=b/c and a,b,c>0 then show that, (a^2+b^2)(b^2+c^2)=(ab+bc)^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)= ( ab + bc + cd)^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) = (ab+bc+cd)^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) = (ab+bc+cd)^2