Question

Find x if x=9+4√5 then find √x-1/x

Answer 1

Step-by-step explanation:

x=9+4 root 5

=9+4 (2.236)

=9+8.944

x=17.944

root x -1/x=root (17.944)-1/17.944

=4.23-0.055

=4.175

Answer 2

Answer:

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

To find

$x - \frac{1}{x}$

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

Rationalize the denominator:-

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

$= \frac{9 - \sqrt[4]{5} }{( {9})^{2} - ( { \sqrt[4]{5} } })^{2} }$

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

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

According to question:-

$x - \frac{1}{x}$

$9 + \sqrt[4]{5} - (9 - \sqrt[4]{5} )$

$= 9 + \sqrt[4]{5} - 9 + \sqrt[4]{5}$

$= \sqrt[4]{5} + \sqrt[4]{5}$

$= 2( \sqrt[4]{5} )$

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