Question

If x= (√3+√2)/(√3-√2) , then find x+1/x

Answer 1

`6-2√(6)`

Explanation:

`x=(√(3)+√(2))/(√(3)-√(2))`

`x= (\left(√(3)+√(2)\right)\left(√(3)+√(2)\right))/(\left(√(3)-√(2)\right)\left(√(3)+√(2)\right))`

`x=(5+2√(6))/(1)`

`x=5+2√(6)`

Substitute
`5+2√(6)` for
`x`.

`(x+1)/(x)`

`(5+2√(6)+1)/(5+2√(6))`

`(6+2√(6))/(5+2√(6))`

`(\left(6+2√(6)\right)\left(5-2√(6)\right))/(\left(5+2√(6)\right)\left(5-2√(6)\right))`

`(6-2√(6))/(1)`

`6-2√(6)`