Question

If (a+b)/(b+c) = (c+d)/(d+a) then show that either a= c or a+b+c+d= 0

Answer 1

Hi--------=====


(a+b)/(b+c)=(c+d)/(d+a)

cross multiple
(d+a)(a+b)=(b+c)(c+d)


da+bd+a^2+ab=bc+bd+c^2+cd

bd is cancel
so
da+a^2+ab=bc+c^2+cd

take a common from lhs and c from rhs

a(d+a+b)=c(b+c+d)

above equation is only possible when

a=c

or
b+c+d=-a

a+b+c+d=0

hope u got ur answer

Answer 2

(a+b)/(b+c)=( c+d)/(d+a)
........cross multiple....
(d+a)(a+b)=(b+c)(c+d)
da+bd+a^2+ab=bc+bd +c^2+ cd

.............so. bd is cancelled....
So........
da+a^2+ab+=bc+c^2+cd
..............take A comman from LHS and C from RHS .
a(d+a+b) =c (b+c+d)

....,.............above equation is only possible when
A =c
......a+b+c+d=0


....................may be this can help you to got ur answer........