Question

x=3-2√2 find x^2+1/X^2​

Answer 1

Answer:

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

Step-by-step explanation:

$x = 3 - 2 \sqrt{2} \\ {x}^{2} + \frac{1}{ {x}^{2} } \\ = {(3 - 2 \sqrt{2}) }^{2} + \frac{1}{ {(3 - 2 \sqrt{2} )}^{2} } \\ = 9 + 8 - 12 \sqrt{2} + \frac{1}{9 + 8 + 12 \sqrt{2} } \\ = 17 - 12 \sqrt{2} + \frac{1}{17 - 12 \sqrt{2} } \\ = \frac{ {(17 - 12 \sqrt{2} )}^{2} + 1}{17 - 12 \sqrt{2} } \\ = \frac{289 + 288 - 408 \sqrt{2} + 1}{17 - 12 \sqrt{2} } \\ = \frac{578 - 408 \sqrt{2} }{17 - 12 \sqrt{2} } \\ = \frac{34(17 - 12 \sqrt{2}) }{(17 - 12 \sqrt{2}) } \\ = 34$