Question

If x>0 and x = 1/x - 1 then find the value of x.​

Answer 1

Answer:

$\large\boxed{\sf{x = \dfrac{ \sqrt{5} -1}{2}}}$

Step-by-step explanation:

Given an equation such that,

$x = \dfrac{1}{x} - 1$

Also, x > 0

To find the value of x

Let's solve the given equation.

Therefore, we will get,

$= > x = \dfrac{1 - x}{x}$

Now, doing cross multiplication, we get,

$= > {x}^{2} = 1 - x \\ \\ = > {x}^{2} + x - 1 = 0$

Now, it's a quadratic equation.

So, we have the value of x,

$= > x = \dfrac{ - 1 \pm \sqrt{ {(1)}^{2} - 4(1)( - 1) } }{2(1)} \\ \\ = > x = \dfrac{ - 1 \pm \sqrt{1 + 4} }{2} \\ \\ = > x = \dfrac{ - 1 \pm \sqrt{5} }{2}$

Thus, the possible values of $x = \dfrac{ - 1 \pm \sqrt{5} }{2}$

But, as given in question x > 0

Hence, the required value of $x = \dfrac{ \sqrt{5} - 1 }{2}$