Question

please answer my question fast ​

Answer 1

Answer:

-2320.

Step-by-step explanation:

Given x= 1-√2.

We have to find the value of

$( x - \frac{1}{x} ) ^{4}$

Now, solution:-

$(1 - \sqrt{2} - \frac{1}{1 - \sqrt{2} }) ^{4} \\ = ( \frac{1 - 2 \sqrt{2 } + 2 - 1 }{1 - \sqrt{2} } ) ^{4} \\ = ( \frac{2 + 2 \sqrt{2} }{1 - \sqrt{2} } ) ^{4} \\ = ( \frac{2 + 2 \sqrt{2} + 2 \sqrt{2} + 4 }{1 - 2} ) ^{4} \\ = ( \frac{6 + 4 \sqrt{2} }{ - 1} ) ^{4} \\ = - 1( 1296 + 1024) \\ = - 1296 - 1024 = - 2320$

HOPE IT HELPS...