Question

If `(7m + 2n)/(7m - 2n) = 5/3`, use properties of proportion to find:

1. m : n
2. `(m^2 + n^2)/(m^2 - n^2)`

Answer 1

i. `(7m + 2n)/(7m - 2n) = 5/3`

Applying componendo and dividendo, we get

`(7m + 2n + (7m - 2n))/(7m + 2n - (7m - 2n)) = (5 + 3)/(5 - 3)`

`=> (14m)/(4n) = 8/2`

`=> (7m)/(2n) = 4/1`

`=> m/n = 8/7`

`=>` m : n = 8 : 7

ii. `m/n = 8/7 => m^2/n^2 = 8^2/7^2`

Applying componendo and dividendo, we get

`=> (m^2 + n^2)/(m^2 - n^2) = (8^2 + 7^2)/(8^2 - 7^2)`

`=> (m^2 + n^2)/(m^2 - n^2) = (64 + 49)/(64 - 49)`

`=> (m^2 + n^2)/(m^2 - n^2) = 113/15`