x-1-x-3-x-x-1-

Question Number 164177 by mathlove last updated on 15/Jan/22

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

\frac{x}{\sqrt{x} + 1} = ?

Answered by mr W last updated on 15/Jan/22

x^{2} - 3 x + 1 = 0

x = \frac{3 \pm \sqrt{5}}{2} = \frac{6 \pm 2 \sqrt{5}}{4} = {(\frac{\sqrt{5} \pm 1}{2})}^{2}

\sqrt{x} = \frac{\sqrt{5} \pm 1}{2}

\frac{x}{\sqrt{x} + 1} = \frac{\frac{3 \pm \sqrt{5}}{2}}{\frac{\sqrt{5} \pm 1}{2} + 1} = \frac{3 \pm \sqrt{5}}{2 + \sqrt{5} \pm 1} = 1 o r \sqrt{5} - 2

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