Question

if x=3-2root 2 find value of x-1/x

Answer 1

Solution :

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Given :

x = 3 - 2√2

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To Find :

The value of : $x - \frac{1}{x}$

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We know that,.


x = 3 - 2√2,

Hence,

⇒ $x - \frac{1}{x}$

⇒ $\frac{x^2 - 1}{x}$  (By cross-multiplication,.)

Substituting the value of x,.

We get,.

⇒ $\frac{(3 - 2 \sqrt{2} )^2 - 1}{3 - 2 \sqrt{2} }$

⇒ $\frac{(3)^2 + (2 \sqrt{2})^2 - 2(3)(2 \sqrt{2}) - 1 }{3 - 2 \sqrt{2} }$

⇒ $\frac{9 + 8 -12 \sqrt{2} - 1 }{3 - 2 \sqrt{2} }$

⇒ $\frac{16 - 12 \sqrt{2} }{3 - 2 \sqrt{2} }$

By taking conjugate,.

We get,

⇒ $\frac{16 - 12 \sqrt{2} }{3 - 2 \sqrt{2} } ( \frac{3 + 2 \sqrt{2} }{3 + 2 \sqrt{2} } )$

⇒ $\frac{(16 - 12 \sqrt{2} )( 3 + 2 \sqrt{2} )}{(3- 2 \sqrt{2})(3 + 2 \sqrt{2} ) }$

⇒ $\frac{16(3) + 16(2 \sqrt{2} ) - 12 \sqrt{2}(3) - 12 \sqrt{2}(2 \sqrt{2} ) }{(3)^2 - (2 \sqrt{2} )^2}$

⇒ $\frac{48 - 36 \sqrt{2} + 32 \sqrt{2} - 48 }{9 - 8}$

⇒ $\frac{ -4 \sqrt{2} }{1}$

⇒ -4√2

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                                   Hope it Helps !!

Answer 2

The answer is given in the attachment.

Thank you for your question.