Maharashtra State BoardSSC (English Medium) 9th Standard
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If 15 a 2 + 4 B 2 15 a 2 − 4 B 2 = 47 7 Then Find the Value of Following Ratio. - Algebra

Sum

If `(15a^2 + 4b^2)/( 15a^2 - 4b^2) = 47/7` then find the value of following ratio.
`a/b`

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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) = 27/20`

⇒ `a^2/b^2 = (27 xx 8)/( 20 xx 30) = 9/25`

⇒ `a/b = sqrt( 9/25) = 3/5`

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APPEARS IN

Balbharati Mathematics 1 Algebra 9th Standard Maharashtra State Board
Chapter 4 Ratio and Proportion
Practice Set 4.3 | Q 2.1 | Page 70
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