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प्रश्न
If `bb((15a^2 + 4b^2)/( 15a^2 - 4b^2) = 47/7 )` then find the value of the following ratio.
`(7a - 3b)/ (7a + 3b)`
उत्तर
`(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) = 9/25`
⇒ `a/b = sqrt( 9/25)`
∴ `a/b = 3/5`
`therefore ( 7a - 3b)/( 7a + 3b)`
= `[(7a)/b - (3b)/b]/[(7a)/b + (3b)/b]`
= `[ 7 xx 3/5 - 3]/[7 xx 3/5 + 3] ...(a/b = 3/5)`
= ` [(21 -15)/5]/[(21 + 15)/5]`
= `6/36`
= `1/6`
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