Question

if x is equals to 5 minus root 24 then find x sqrt +1/x sqrt ​

Answer 1

Step-by-step explanation:

$x = 5 - \sqrt{24}$

to find:-

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

solution:-

$\frac{1}{x} = \frac{1}{5 - \sqrt{24} } \\ \\ \frac{1}{x} = \frac{1}{5 - \sqrt{24} } \times \frac{5 + \sqrt{24} }{5 + \sqrt{24} } \\ \\ = \frac{5 + \sqrt{24} }{ {5 }^{2} - {( \sqrt{24)} }^{2} } = 5 + \sqrt{24}$

NOW,

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

so,

${x}^{2} + \frac{1}{ {x}^{2} } = (5 + \sqrt{24 } + 5 - \sqrt{24} ) > 2- 2 \\ = 100 - 2 = 98$