If x^2 - 3x + 1= 0 and x > 1, then the value of (x - \frac{1}{x})

Question 132

If $$x^2 - 3x + 1= 0$$ and x > 1, then the value of $$(x - \frac{1}{x})$$

Solution

Expression : $$x^2 - 3x + 1= 0$$

=> $$x^2 + 1 = 3x$$

Dividing by $$(x)$$ on both sides

=> $$x + \frac{1}{x} = 3$$

$$\because (x - \frac{1}{x})^2 = (x + \frac{1}{x})^2 - 4$$

=> $$x - \frac{1}{x} = \sqrt{9 - 4}$$

=> $$(x - \frac{1}{x}) = \pm\sqrt{5}$$

Create a FREE account and get: