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If (4m + 3n)/(4m - 3n) = 7/4 Use Properties of Proportion to Find (2m^2 - 11n^2)/(2m^2 + 11n^2) - Mathematics

If `(4m + 3n)/(4m - 3n) = 7/4` use properties of proportion to find `(2m^2 - 11n^2)/(2m^2  + 11n^2)`

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Solution

`m/n = 11/4`

`m^2/n^2 = 121/16`

`(2m^2)/(11n^2) = (2 xx 121)/(11 xx 16)`   (Multiplying both sides by 2/11)

`(2m^2)/(11n^2) = 11/8`

`(2m^2 + 11n^2)/(2m^2 - 11n^2) = (11 + 8)/(11 - 8)` (Applying  componendo and divdendo)

`(2m^2 + 11n^2)/(2m^2  - 11n^2) = 19/3`

`(2m^2 - 11n^2)/(2m^2 + 11n^2) = 3/19`   (Applying invertendo)

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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 7 Ratio and Proportion (Including Properties and Uses)
Exercise 7 (D) | Q 17.2 | Page 102
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