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Question
If `(7"m" + 2"n")/(7"m" - 2"n") = 5/3` use properties of proportion to find:
(i) m : n
(ii) `("m"^2 + "n"^2)/("m"^2 - "n"^2)`
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Solution
(i) `(7"m" + 2"n")/(7"m" - 2"n") = 5/3`
Pplying Componendo and dividendo, we get
`(7"m" + 2"n" + 7"m" - 2"n")/(7"m" - 2"n"- 7"m" + 2"n") = (5 + 3)/(5 - 3)`
⇒ `(14"m")/(4"n") = 8/2`
⇒ `"m"/"n" = (8 xx 4)/(2 xx 14)`
⇒ `"m"/"n" = 8/7`
⇒ m : n = 8 : 7
(ii) From i,
`"m"/"n" = 8/7`
⇒ `"m"^2/"n"^2 = 64/49`
Pplying Componendo and Dividendo,we get
`("m"^2 + "n"^2)/("m"^2 - "n"^2) = (64 + 49)/(64 - 49)`
⇒ `("m"^2 + "n"^2)/("m"^2 - "n"^2) = (64 + 49)/(64 - 49)`
⇒ `("m"^2 + "n"^2)/("m"^2 - "n"^2) = 113/15 = 7 8/15`
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