Question

If a,b,c,d are in G.P then (a+b+c+d)^2=?

Answer 1

@ganeshie8

Answer 2

does it lead to much simplification??
all you can use is
ad = bc

Answer 3

or maybe write, terms as
a,ar, ar^2, ar^3
(b=ar, c=ar^2,d=ar^3)

Answer 4

I have the answer it is

(a+b)^2+(c+d)^2+2(b+c)^2

Answer 5

ahh that looks neat

Answer 6

for the starters, just treat a+b as say A
c+d as say B
and expand (A+B)^2

Answer 7

2AB= 2(a+b)(c+d)
multiply them out and use the fact that ac = bd

Answer 8

ad = bc***

Answer 9

Tried it. But I am not able to progress.

Answer 10

ok,
ac+ad+bc+bd should equal (b+c)^2

ac +bc+bc+bd
-----------------------------------------
so, ac+bd should equal b^2+c^2

we have a/b=b/c=c/d
here ac= b^2 and bd = c^2
have a look :)

Answer 11

that gives below result :

if a,b,c,d are in GP, then a+b, b+c, c+d also will be in GP

Answer 12

Now that makes sense!! Thank you!! :)

Answer 13

welcome ^_^