Question

x+1/x=√3 then value of 3x/x^2-1​

Answer 1

3x/(x² - 1)  = 3 ( (√3  ± i )/2)³  if x+1/x=√3

Step-by-step explanation:

x  + 1/x  = √3

Squaring both sides

=> x²  + 1/x²  + 2x(1/x)  = 3

=> x²  + 1/x²   + 2 = 3

=> x² - 1  = 1/x²

3x/(x² - 1)  =  3x/(1/x²)

= 3x³

x  + 1/x  = √3

=> x² + 1 = √3 x

=> x² - √3 x + 1  =0

=> x  = (√3  ± √(3 - 4))/2

=> x = (√3  ± i )/2

3x³ = 3 ( (√3  ± i )/2)³

3x/(x² - 1)  = 3 ( (√3  ± i )/2)³  if x+1/x=√3

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