Question

x= 9+4√5 find the value of √x- 1/√x. be quick please

Answer 1

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

Now,

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

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

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

$= \ \textgreater \ 9 - 4 \sqrt{5}$

Now,

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

$= \ \textgreater \ x + \frac{1}{x} = 18$

$= \ \textgreater \ x + \frac{1}{x} - 2 = 16$

$= \ \textgreater \ ( \sqrt{x} - \frac{1}{ \sqrt{x} } )^2 = 16$

$= \ \textgreater \ \sqrt{x} - \frac{1}{ \sqrt{x} } = 4$



Hope this helps!

Answer 2

Answer :

Given,

x = 9 + 4√5

= 4 + 4√5 + 5

= 2² + (2 × 2 × √5) + (√5)²

= (2 + √5)²

So, √x = 2 + √5

Now, 1/√x

= 1/(2 + √5)

= (2 - √5)/{(2 + √5)(2 - √5)}

= (2 - √5)/(4 - 5)

= (2 - √5)/(- 1)

= - 2 + √5

Thus,

√x - 1/√x

= (2 + √5) - (- 2 + √5)

= 2 + √5 + 2 - √5

= 4

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