Question

If `(1 + x + x^2)/(1 - x + x^2) = (62(1 + x))/(63(1 - x))` then the value of x is ______.

पर्याय

• `1/5`

• 5

• 3

• `1/3`

Answer 1

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`