Question

solve fast plz and answer me
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Answer 1

$Question:$

$If x = 3+2\sqrt{2} \\\\then \sqrt{x} -\frac{1}{\sqrt{x} } = ?$

$Answer :$

$x = 3+2\sqrt{2}\\\\= 1^{2} + (\sqrt{2}) ^{2} + 2 * 1*\sqrt{2} \\= (1+\sqrt{2} )^{2} .$

Now ,

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

Thanks..

Answer 2

Answer:

2

Step-by-step explanation:

x = 3 + 2√2

√x = √( 3 + 2√2 )

⇒ √x = √( 2 + 2√2 + 1 )

⇒ √x = √( √2 + 1 )²

⇒ √x = √2 + 1

1/√x = 1/( √2 + 1 )

⇒ 1/√x = 1/(√2 + 1 ) × ( √2 - 1 )/(√2 - 1 )

⇒ 1/√x = (√2 - 1 ) / ( 2 - 1 ) = √2 - 1

Hence √x - 1/√x

⇒ √2 + 1 - ( √2 - 1 )

⇒ 2