If x is a rational number and \frac{(x+1)^3-(x-1)^3}{(x+1)^2-(x-1)^2} = 2, then the sum of numerator and denominator of x is

SSC CGL 19 Oct 2014 Shift 2 Paper

Question : 122 of 200

Marks: +1, -0

If x is a rational number and

{(x+1)^3-(x-1)^3}/{(x+1)^2-(x-1)^2}

= 2, then the sum of numerator and denominator of x is

Solution:

⇒

{(x^3+3x^2+3x+1)-(x^3-3x^2+3x-1)}/{(x^2+2x+1)-(x^2-2x+1)}

= 2
⇒

{x^3+3x^2+3x+1-x^3+3x^2-3x+1}/{x^2+2x+1-x^2+2x-1}

= 2
⇒

{6x^2+2}/{4x}

= 2
⇒

{3x^2+1}/{4x}

= 1 ⇒

3x^2

+ 1 = 4x
⇒ 3x2 – 4x + 1 = 0
⇒

3x^2

– 3x – x +1 = 0
⇒ 3x (x – 1) – 1(x – 1) = 0
⇒ (3x – 1) (x – 1) = 0
⇒ x =

1/3

or 1
∴ Required answer = 1 + 3 = 4

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