Question

if x=4+sq root 15,find the value of (i)x (ii)x+1/x

Answer 1

x=4+√15
1/x= 1/(4+√15) = 4-√15
to find x + 1/x
x+1/x = (4+√15 + 4 - √15 )
x+1/x = 8

Answer 2

$x = 4+ \sqrt{15}$

$\frac{1}{x} = \frac{1}{4+ \sqrt{15} }$

$\frac{1}{x} = \frac{1}{4+ \sqrt{15} } * \frac{4- \sqrt{15}}{4- \sqrt{15} } = \frac{4- \sqrt{15}}{16-15} = 4- \sqrt{15}$

$x + \frac{1}{x} = 4+ \sqrt{15} + 4- \sqrt{15} = 8$