Question

if x= 9+4√5 then x-1/x​

Answer 1

Answer:

$8 \sqrt{5}$

Step-by-step explanation:

$x = 9 + 4 \sqrt{5}$

$\frac{1}{x} = \frac{1}{9 + 4 \sqrt{5} } \times \frac{9 - 4 \sqrt{5} }{9 - 4 \sqrt{5} }$

$= \frac{9 - 4 \sqrt{5} }{81 - 80} = 9 - 4 \sqrt{5}$

Thus,

$x - \frac{1}{x} = 9 + 4 \sqrt{5} - 9 + 4 \sqrt{5}$

$= 8 \sqrt{5}$

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