Question

If x=3+2√2, find the value of (√x-1/√x)​

Answer 1

Step-by-step explanation:

hope you like my answer

Answer 2

Given,

 x=3+2√2

To find,

(√x-1/√x)​

Solution,

$x=3+2\sqrt{2} \\\\=> \frac{1}{x} = \frac{1}{3+2\sqrt{2}}\\\\ =\frac{1}{3+2\sqrt{2}} * \frac{3-2\sqrt{2}}{3-2\sqrt{2}} \\\\= \frac{3 - 2\sqrt{2}}{(3)^{2} - (2\sqrt{2})^{2} } \\\\=\frac{3 - 2\sqrt{2} }{9 - 8} \\\\\frac{1}{x} = 3 - 2\sqrt{2} \\\\So,\\\\ x+\frac{1}{x} = 3+2\sqrt{2} + 3 - 2\sqrt{2}\\\\= 3 + 3 \\\\Hence, {x} + \frac{1}{x} = 6$

Subtracting 2 from both sides

$=> x + \frac{1}{x} - 2 = 6 -2\\\\=> {(\sqrt{x})^{2} + \frac{1}{(\sqrt{x})^{2} } - 2.\sqrt{x} .\frac{1}{\sqrt{x} } \\= 4$

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

ANS - 2