Question

if x= 3+root over8 ,then find the value of x²+1/x²​

Answer 1

Step-by-step explanation:

$x = 3 + \sqrt{8}$

Then,

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

$= 9 + 6 \sqrt{8} + 8 + \frac{1}{9 + 6 \sqrt{8} + 8}$

$= 17 + 6 \sqrt{8} + \frac{1}{17 + 6 \sqrt{8} }$

$= \frac{ {(17 + 6 \sqrt{8} )}^{2} + 1}{17 + 6 \sqrt{8} }$

$= \frac{289 + 204 \sqrt{8} + 288 + 1}{17 + 6 \sqrt{8} }$

$= \frac{578 + 204 \sqrt{8} }{17 + 6 \sqrt{8} }$