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If x is a rational number and ((x + 1)...

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

A

3

B

4

C

5

D

7

Text Solution

Verified by Experts

The correct Answer is:
B
`((x+1)^3 - (x-1)^3)/((x + 1)^2 - (x - 1)^2) = 2`
`implies (6x^2 + 2)/(4x) = 2`
`implies 3x^2 + 1 = 4x`
`implies 3x^2 - 4x + 1 = 0`
`implies x = (4 pm sqrt(16 - 12))/(6) = (4 pm 2)/6`
`implies x = 1, 1/3`
यदि `x = 1 `हो तो
अंश तथा हर का योग `= 1+ 1 = 2` (विकल्प में नहीं है) यदि `x = 1/3` हो, तो
अंश तथा हरों का योग `= 1+ 3 = 4 `
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