Question

If x = 5 - 2√6 then find the value of x + 1/x.

Answer 1

Answer:

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attempted....

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Answer 2

given

$x = 5 - 2 \sqrt{6}$

we can write

$\frac{1}{x} = \frac{1}{5 - 2 \sqrt{6} }$

rationalizing denominator we get

$\frac{1}{x} = \frac{5 + 2 \sqrt{6} }{25 - 24} \\ \\ \frac{1}{x} = 5 + 2 \sqrt{6}$

Now

$x + \frac{1}{x} = 10$