Question

if x = 4+2√3 find x+1/x​

Answer 1

x=4+2√3

According to question

x+1/x=4+2√3+1/4+2√3

By rationalising the denominator

=5+2√3/4+2√3×4-2√3/4-2√3

=(5+2√3)(4-2√3)/(4)^2-(2√3)^2

=20-10√3+8√3-12/16-12

=8-2√3/4

=2(4-√3)/4

=4-√3/2