Question

of x=3+2√2 then find the value of √x-1/√x​

Answer 1

Answer:

14-10√2

Step-by-step explanation:

following the attachment

Answer 2

given

$x = 3 - 2 \sqrt{2}$

so we can write

$\frac{1}{x} = \frac{1}{3 - 2 \sqrt{2} }$

rationalizing denominator we get

$\frac{1}{x} = \frac{3 + 2 \sqrt{2} }{9 - 8} \\ \\ \frac{1}{x} = 3 + 2 \sqrt{2}$

Now

$x + \frac{1}{x} = 3 - 2 \sqrt{2} + 3 + 2 \sqrt{2} \\ \\ x + \frac{1}{x} = 6$

subtracting 2 from both sides

$x + \frac{1}{x} - 2 = 4 \\ \\ ( \sqrt{x} - \frac{1}{ \sqrt{x} } ) ^{2} = 4 \\ \\ \sqrt{x} - \frac{1}{ \sqrt{x} } = 2$