Question

if ( a+b ) ÷ c = ( b+c ) ÷ a = ( c+a ) ÷ b then prove that each ratio equal to 2 or -1

Answer 1

let
(a+b)/c=(b+c)/a=(c+a)/b=k

(a+b)/c=k=>a+b=ck......(1)

(b+c)/a=k=>b+c=ak...(2)

(c+a)/b=k=>c+a=bk...(3)


by eqn (1)-(2)

a-c=k(c-a)......(A)=>k=-1


by eqn (2)-(3)

b-a=k(a-b).....(B)=>k=-1

by eqn (1)-(3)

b-c=k(c-b)....(C)=>k=-1

k= -1 is proved