Question

If x =3+√8 ,find x^4+1/x^4​

Answer 1

Answer:

answer is 32

Step-by-step explanation:

given in pic

Answer 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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