Question

if x=2+root7 then find the value of x+1/x

Answer 1

(2+_/7)+1/(2+_/7)
=(2+_/7)+{(2-_/7)/(-3)}
=(2+_/7)-{(2-_/7)/3}
=2_/7 / 3
~(2 root 7 by 3)

Answer 2

given x= 2 + √7
x= √7+2---(1)

1/x = 1/(√7 +2) 
= (√7 -2)/[(√7 +2) (√7 -2)  ]

= (√7 -2 )/ [ (√7)² - 2²] { ∵ (a+b)(a-b) = a²-b²}

= (√7 -2)/(7-4)
= (√7 -2 ) /3 ---(2)

x+1/x = (1) +(2)

=√7 +2 + (√7 -2)/3
= [3(√7 +2) +√7 -2]/3
= (3√7 +6 +√7 -2) /3
= (4√7 +4)/3
=4/3(√7 +1)