Question

If `(a + b)/(am + bn)= (b + c)/(mb + nc )= (c + a)/(mc + na)` prove that each of theseccc `2/(m+n)`provided  a + b + c ≠ 0

Answer 1

`(a + b)/(am + bn)= (b + c)/(mb + nc )= (c + a)/(mc + na)` `

`" sumof antecedents"/"sumof consequents"`

= `(a + b+b+c+c+a)/(am + bn +mb+ nc +mc+na)`

= `(2(a+b+c))/(m(a+b+c) =n (a+b+c))`

= `2/(m+n)`