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प्रश्न
If `(3a + 7b)/( 3a - 7b) = 4/3` then find the value of the ratio `(3a^2 - 7b^2)/(3a^2 + 7b^2)`.
उत्तर
`( 3a + 7b)/( 3a - 7b) = 4/3`
Applying componendo and dividendo, we get
`[( 3a + 7b) +( 3a - 7b)]/[( 3a + 7b) - ( 3a - 7b)] = (4+3)/(4-3)`
⇒ `[3a + 7b + 3a -7b]/[ 3a + 7b - 3a + 7b] = 7/1`
⇒ `(6a)/(14b)= 7/1`
⇒ `a/b = ( 14 xx 7)/6 = 49/3` ...(I)
Squaring both sides,
`a^2/b^2=2401/9`
Multiplying both sides by `3/7`
`3/7xxa^2/b^2=3/7xx2401/9`
`(3a^2)/(7b^2)=343/3`
`(3a^2 + 7b^2)/(3a^2 - 7b^2)=(343+3)/(343-3)` ...(using componendo and dividendo)
`(3a^2 + 7b^2)/(3a^2 - 7b^2)=346/340=173/170`
∴ `(3a^2 - 7b^2)/(3a^2 + 7b^2)=170/173`
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