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Question
Solve for x: `(1 + x + x^2)/(1 - x + x^2) = (62(1 + x))/(63(1 - x))`
Sum
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Solution
It is given that:
`(1 + x + x^2)/(1 - x + x^2) = (62(1 + x))/(63(1 - x))`
⇒ `63(1 - x)(1 + x + x^2) = 62(1 + x)(1 - x + x^2)`
⇒ `63(1 - x^3) = 62(1 + x^3)`
⇒ 63 − 63x3 = 62 + 62x3
⇒ 63 − 62 = 62x3 + 63x3
⇒ 1 = 125x3
⇒ x3 = `1/125`
⇒ x = `root3 (1/125)`
⇒ x = `1/5`
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