Question

Inequalities #1
Four integers a, b, c and d (where b>0) satisfy three conditions a+b=c, b+c=d and c+d=a. Find the greatest possible value of a+b+c+d

Answer 1

a+b =c and c+d =a
so a+b+c+d = a+c
=> b = -d
and b+c = d
=> c= 2d
so a =3d
so a+c = 5d
now b>0
thus d<0
max d = just LHL of 0
so max for a+b+c+d = LHL of 0

Answer 2

or in layman language,,its 0.

Answer 3

I see!! I didn't notice that last part!!! Thanks :)

Answer 4

glad to help ^_^