Find-2-2-8-6-4-2-8-2-2-8-

Question Number 207226 by hardmath last updated on 10/May/24

Find : \frac{{(2 - \sqrt{2})}^{8} \cdot {(6 + 4 \sqrt{2})}^{8}}{{(2 + \sqrt{2})}^{8}} = ?

Answered by Sutrisno last updated on 10/May/24

{(\frac{(2 - \sqrt{2}) (6 + 4 \sqrt{2})}{2 + \sqrt{2}})}^{8}

{(\frac{(2 - \sqrt{2}) (6 + 4 \sqrt{2})}{2 + \sqrt{2}} . \frac{2 - \sqrt{2}}{2 - \sqrt{2}})}^{8}

{(\frac{(4 - 4 \sqrt{2} + 2) (6 + 4 \sqrt{2})}{4 - 2})}^{8}

{(\frac{(6 - 4 \sqrt{2}) (6 + 4 \sqrt{2})}{2})}^{8}

{(\frac{36 - 32}{2})}^{8}

{(\frac{4}{2})}^{8} = 256

Answered by Rasheed.Sindhi last updated on 10/May/24

{(\frac{(2 - \sqrt{2}) \cdot (6 + 4 \sqrt{2})}{(2 + \sqrt{2})})}^{8}

= {(\frac{(2 - \sqrt{2}) \cdot ({(2 + \sqrt{2})}^{2}}{(2 + \sqrt{2})})}^{8}

= {((2 - \sqrt{2}) (2 + \sqrt{2}))}^{8}

= {(4 - 2)}^{8} = 256

Commented by hardmath last updated on 10/May/24

thank you professors