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प्रश्न
Given that `(a^3 + 3ab^2)/(b^2 + 3a^2b) = (63)/(62)`.
Using Componendo and Dividendo find a : b.
उत्तर
We have
`(a^3 + 3ab^2)/(b^2 + 3a^2b) = (63)/(62)`
App. compoenedo and dividendo
`(a^3 + 3ab^2 + b^3 + 3a^2b)/(a^3 + 3ab^2 - b^3 - 3a^2b) = (63 + 62)/(63 - 62)`
`(a^3 + 3ab^2 + b^3 + 3a^2b)/(a^3 + 3ab^2 - b^3 - 3a^2b) = (125)/(1)`
`(a + b)^3/(a - b)^3 = (125)/(1)`
`(a + b)/(a - b) = (5)/(1)`
Again Applying Componendo & Dividendo
`(a + b + a - b)/(a + b - a + b) = (5 + 1)/(5 - 1)`
`(2a)/(2b) = (6)/(4)`
a : b = 3 : 2
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