Question

x^2 =17+12√2 then find x^2-1÷x^2.​

Answer 1

Answer:

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

Step-by-step explanation:

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