Question

$if \: x = 3 - 2 \sqrt{2 \:} find \: {x}^{4} - \: \frac{ 1}{ {x}^{4} }$

Please give answer with explanation ​

Answer 1

Step-by-step explanation:

x+

x

1

=3−2

2

+

3−2

2

1

x

1

=

3−2

2

1

×

3+2

2

3+2

2

=

1

3+2

2

x+

x

1

=3−2

2

+3+2

2

=6

Squaring on both sides,

(x+

x

1

)

2

=36

x

2

+

x

2

1

=36−2

⇒x

2

+

x

2

1

=34

Squaring on both sides,

(x

2

+

x

2

1

)

2

=(34)

2

x

4

+

x

4

1

=1156−2

⇒x

4

+

x

4

1

=1154.