Question

If x=3-2√2,then (x-1/x)2=?

Answer 1

Answer:  14/13

Step-by-step explanation:

x = 3 - 2√2  ( Given )

( x - 1/ x)²

= ( 3 - 2√2 - 1 / 3 - 2 √2)²

= ( 3 - 2√2 - 1)² / (3 - 2√2)²

= ( (3)²+(-2√2)² + (-1)² / ( (3)² + (-2√2)²

= 9 + 4 + 1 / 9 + 4

= 14/13

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Answer 2

Step-by-step explanation:

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

$x - \frac{1}{x} = 3 - 2 \sqrt{2} - 3 - 2 \sqrt{2} \\ \\ x - \frac{1}{x} = -4\sqrt{2}$

squaring both sides

$( {x - \frac{1}{x} })^{2} = ({-4\sqrt{2}})^{2} \\ \\ ( {x - \frac{1}{x} })^{ 2} =32$