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प्रश्न
Solve for `x : 16((a - x)/(a + x))^3 = (a + x)/(a - x)`
उत्तर
`x : 16((a - x)/(a + x))^3 = (a + x)/(a - x)`
⇒ `((a + x)/(a - x)) xx ((a + x)/(a - x))^3` = 16
⇒ `((a + x)/(a - x))^4` = 16 = (±2)4
⇒ `(a + x)/(a - x)` = ±2
When `(a + x)/(a - x) = (2)/(1)`
Applying componendo and dividendo,
`(a + x + a - x)/(a + x - a + x) = (2 + 1)/(2 - 1)`
⇒ `(2a)/(2x) = (3)/(1)`
⇒ `a/x = (3)/(1)`
⇒ 3x = a
∴ x = `a/(3)`
When `(a + x)/(a -x) = (-2)/(1)`
Applying componendo and dividendo
`(a + x + a - x)/(a + x - a + x) = (-2 + 1)/(-2 - 1)`
⇒ `(2a)/(2x) = (-1)/(3)`
⇒ `a/x = (1)/(3)`
⇒ x = 3a
Hence x = `a/(3), 3a`.
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