Math, asked by mehulg2005, 11 months ago

If x =3+√8 ,find x^4+1/x^4​

Answers

Answered by saipriya0420
1

Answer:

answer is 32

Step-by-step explanation:

given in pic

Attachments:
Answered by 14ueee022
1

Answer:

 {x}^{4}  +  \frac{1}{ {x}^{4} } = 1156

Step-by-step explanation:

x = 3 +  \sqrt{8}

 \frac{1}{x}  =  \frac{1}{(3 +  \sqrt{8} )}

Multiply

 \frac{1}{(3 +  \sqrt{8} )}   \times \frac{(3 -  \sqrt{8} )}{(3 -  \sqrt{8}) }

 \frac{1}{x}  =  \frac{(3 -  \sqrt{8}) }{( {3}^{2}) - (  { \sqrt{8} }^{2} )  }

 \frac{1}{x}  =  \frac{(3 -  \sqrt{8} )}{9 - 8}

 \frac{1}{x}  = (3 -  \sqrt{8} )

 ( {x}^{2}  +  \frac{1}{ {x}^{2} }) ^{2}  =  {x}^{4}  +  \frac{1}{ {x}^{4} }

 {x}^{2}  =  {(3 +  \sqrt{8} )}^{2}

 {x}^{2}  =  {3}^{2}  + ( \sqrt{8}  )^{2}  + 2(3)( \sqrt{8} )

 {x}^{2}  = 9 + 8 + 6 \sqrt{8}

{x}^{2}  = 17 + 6 \sqrt{8}

  \frac{1}{ {x}^{2} }  = (3  -   \sqrt{8} )^{2}

 \frac{1}{ {x}^{2} }  = 17 - 6 \sqrt{8}

 {x}^{2}  +  \frac{1}{ {x}^{2} }  = 17 + 6 \sqrt{8}  + 17 - 6 \sqrt{8}

 {x}^{2}  +  \frac{1}{ {x}^{2} } = 34

 {x}^{4}  +  \frac{1}{ {x}^{4} }  =  {34}^{2}

 {x}^{4}  +  \frac{1}{ {x}^{4} }  = 1156.

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