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Question
If `bb((15a^2 + 4b^2)/( 15a^2 - 4b^2) = 47/7)` then find the value of following ratio.
`a/b`
Solution
`(15a^2 + 4b^2)/( 15a^2 - 4b^2) = 47/7`
Applying componendo and dividendo, we get
`[(15a^2 + 4b^2) + ( 15a^2 - 4b^2)]/[(15a^2 + 4b^2) - ( 15a^2 - 4b^2)] = [47 + 7]/[47-7]`
⇒ `[15a^2 + 4b^2 +15a^2 - 4b^2]/[15a^2 + 4b^2 - 15a^2 + 4b^2]` =`54/40`
⇒ `(30a^2)/(8b^2) = 54/40`
⇒ `a^2/b^2 = (54 xx 8)/(40 xx 30)`
⇒ `a^2/b^2 = 9/25`
Taking square root both the sides,
⇒ `a/b = sqrt(9/25)`
⇒ `a/b= 3/5`
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