Prove that `Delta=|(1,bc+ad,b^(2)c^(2)+a^(2)d^(2)),(1,ca+bd,c^(2)a^(2)+b^(2)d^(2)),(1,ab+cd,a^(2)b^(2)+c^(2)d^(2))|=(a-b)(a-c)`
`(a-d)(b-c)(b-d)(c-d)`.

If a,b,c,d are in G.P.prove that: (a^(2)+b^(2)),(b^(2)+c^(2)),(c^(2)+d^(2)) are in G.P.(a^(2)-b^(2)),(b^(2)-c^(2)),(c^(2)-d^(2)) are in G.P.(1)/(a^(2)+b^(2)),(1)/(b^(2)+c^(2)),(1)/(c^(2)+d^(2)) are in G.P.(a^(2)+b^(2)+c^(2)),(ab+bc+cd),(b^(2)+c^(2)+d^(2))

If a,b,c,d are in G.P.,prove that (a^(2)-b^(2)),(b^(2)-c^(2)),(c^(2)-d^(2)) are in G.P.and (1)/(a^(2)+b^(2)),(1)/(b^(2)+c^(2)),(1)/(c^(2)+d^(2)) are in G.P

If a,b,c,d are in G.P.prove that: (i) quad (a^(2)-b^(2)),(b^(2)-c^(2)),(c^(2)-d^(2)) are in G.P. (i) (1)/(a^(2)+b^(2)),(1)/(b^(2)+c^(2)),(1)/(c^(2)+d^(2)) are in G.P.

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

If (a)/(b)=(c)/(d) then (a+b)/(a-b)=(c+d)/(c-d),ab=cd ,(a^(2)+b^(2))/(a^(2)-b^(2))=(c^(2)+d^(2))/(c^(2)-d^(2)), ad-dc=0

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

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

If a,b,c are non-zero real numbers then D=det[[b^(2)c^(2),bc,b+cc^(2)a^(2),ca,c+aa^(2)b^(2),ab,a+b]]=(A)abc(B)a^(2)b^(2)c^(2)(C)bc+ca+ab(D)0,