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