Question

7 If x= 3+root 8 , then find value of x² + 1/x^2​

Answer 1

Step-by-step explanation:

$x = 3 + \sqrt{8} \\ \\ then \: the \: value \: of\\ \\ {x}^{2} + \frac{1}{ {x}^{2} } \\ \\ is \\ \\ {(3 + \sqrt{8}) }^{2} + \frac{1}{ {(3 + \sqrt{8}) }^{2} } \\ \\ 9 + 8 + 6 \sqrt{8} + \frac{1}{9 + 8 + 6 \sqrt{8} } \\ \\ 17 + 6 \sqrt{8} + \frac{1}{17 + 6 \sqrt{8} } \\ \\ \frac{ ({17 + 6 \sqrt{8} )}^{2} + 1 }{17 + 6 \sqrt{8} } \\ \\ \frac{289 + 288 + 204 \sqrt{8} + 1}{17 + 6 \sqrt{8} } \\ \\ \frac{578 + 204 \sqrt{8} }{17 + 6 \sqrt{8} } \\ \\ \frac{578 + 408 \sqrt{2} }{17 + 12 \sqrt{2} } \\ \\ \frac{34(17+12\sqrt{2})}{17+12\sqrt{2}}\\ \\ = 34$