Question

$If  \: \ \textless \ br /\ \textgreater \ x = 1 + \sqrt{2 \: } \: show \: that \: {(x - \frac{1}{x} })^{3} = 8$
Please answer fast ...
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Answer 1

Answer:

8

Step-by-step explanation:

$x = 1+\sqrt{2}$

put the value in equation $(x-\frac{1}{x} )^{3}$

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

make denominater is rational

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

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

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

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

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

$(2)^{3}$

$8$

please mark as brainlist

Answer 2

Answer:

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