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If `(7m + 2n)/(7m - 2n) = 5/3`Use Properties of Proportion to Find M:N (M^2 + N^2)/(M^2 - N^2) - Mathematics

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)`

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Solution

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

ByComponendo Divinendo, 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``

2) `m/n = 8/7 => m^2/n^2 = 8^2/7^2`

Applying Componendo Divinendo, 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`

Concept: Componendo and Dividendo Properties
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