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प्रश्न
Solve `(1 + x + x^2)/(1 - x + x^2) = (62(1 +x))/(63(1 + x)`
उत्तर
`(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^3 - 1 + x^3) = (63 + 62)/(63 - 62)`
⇒ `(2)/(2x^3) = (125)/(1)`
⇒ `(1)/(x^3) = (125)/(1)`
⇒ x3 = `(1)/(125)`
= `(1/5)^3`
∴ x = `(1)/(5)`.
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