Question

if x=root5 + root3 / root5 - root3, find the value of x^2 +1/x^2

Answer 1

$x = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } = \frac{( \sqrt{5} + \sqrt{3} )( \sqrt{5} + \sqrt{3} )}{( \sqrt{5} - \sqrt{3} )( \sqrt{5} + \sqrt{3}) } \\ \frac{8 + 2 \sqrt{15} }{5 - 3} = 4 + \sqrt{15}$
$\frac{1}{x} = \frac{1}{4 + \sqrt{15} } = \frac{4 - \sqrt{15} }{(4 + \sqrt{15})(4 - \sqrt{15}) } \\ = \frac{4 - \sqrt{15} }{16 - 15} = 4 - \sqrt{15}$

$x + \frac{1}{x} = 4 - \sqrt{15} + 4 + \sqrt{15} = 16$
${x}^{2} + \frac{1}{ {x}^{2} } = {(x + \frac{1}{x}) }^{2} - 2 \\ = {16}^{2} - 2 = 254$

Answer 2

Answer:

4+4=8

8×8

64-2

=62

thus the answer is this on