Question

If x=2-√5 find 1/x. (Simplify)

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Answer 1

Step-by-step explanation:

x=2-√5

$\frac{1}{x} = \frac{1}{2 - \sqrt{5} }$

$\frac{1}{x} = \frac{1}{2 - \sqrt{5} } \times \frac{2 + \sqrt{5} }{2 + \sqrt{5} }$

$\frac{1}{x} = \frac{2 + \sqrt{5} }{ {2 }^{2} - { \sqrt{5} }^{2} }$

$\frac{1}{x} = \frac{2 + \sqrt{5} }{4 - 5}$

$\frac{1}{x} = \frac{2 + \sqrt{5} }{ - 1}$