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Question
If `(1 + x + x^2)/(1 - x + x^2) = (62(1 + x))/(63(1 - x))` then the value of x is ______.
Options
`1/5`
5
3
`1/3`
MCQ
Fill in the Blanks
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Solution
If `(1 + x + x^2)/(1 - x + x^2) = (62(1 + x))/(63(1 - x))` then the value of x is `bb(1/5)`.
Explanation:
`(1 + x + x^2)/(1 - x + x^2) = (62(1 + x))/(63(1 - x))`
⇒ `((1 - x)(1 + x + x^2))/((1 + x)(1 - x + x^2)) = 62/63`
⇒ `((1 + x)(1 - x + x^2))/((1 - x)(1 + x + x^2)) = 62/63`
⇒ `(1 + x^3)/(1 - x^3) = 63/62`
Applying componendo and dividendo,
⇒ `(1 + x^3 + 1 - x^3)/(1 + x^2 - 1 + x^3) = (63 + 62)/(63 - 62)`
⇒ `2/(2x^3) = 125/1`
⇒ `1/x^3 = 125/1`
⇒ `x^3 = 1/125`
⇒ x = `sqrt(1/25)`
⇒ x = `1/5`
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