Question

If x=7+root40, find the value of root x+1/root x

Answer 1

$\boxed{\mathrm{x=7+\sqrt{40}}} \\\ \mathrm{So,value~of~x+ \frac{1}{x} ? } \\\\ \mathrm{value~of~x=x+7+\sqrt{40}} \\\ \mathrm{value~of~ \frac{1}{x} = \frac{1}{7+\sqrt{40}} x \frac{7-\sqrt{40}}{7-\sqrt{40}} } \\\ ~~~~~~~~~~~~~~= \frac{7-\sqrt40}{(7+\sqrt{40})(7-\sqrt{40})} \\\ ~~~~~~~~~~~~~~= \frac{7-\sqrt{40}}{49-7\sqrt{40}+7\sqrt{40}-40 } \\\ ~~~~~~~~~~~~~~= \frac{7-\sqrt{40}}{9}$

$\mathrm{So:} \\\\ \mathrm{x+ \frac{1}{x} =(7+\sqrt{40})+ \frac{7-\sqrt{40}}{9} } \\\ ~~~~~~~~= \frac{9(7+\sqrt{40})+7-\sqrt{40}}{9} \\\ ~~~~~~~~= \frac{(63+9\sqrt{40})+7-\sqrt{40}}{9} \\\ ~~~~~~~~= \frac{70+8\sqrt{40}}{9} \\\\ \bigstar \mathrm{Please~klik~brainliest~answer } \bigstar$