Question

If x=2+√3,then find the value of x-1/x

Answer 1

A :-) x = 2+_/3
x-1/x = 1/2+_/3
( rationalize the denominator )
x-1/x = 1/2+_/3 x 2 -_/3/2 - _/3
[ ( a + b ) ( a - b ) = a^2 -b^2 ]
x-1/x = 2 - _/3/( 2 )^2 - ( _/3 )^2
x-1/x = 2 - _/3/4 - 3
x-1/x = 2 - _/3/1
x-1/x = 2 - _/3
x-1/x = ( 2+_/3 ) ( 2 - _/3 )
x -1/x = ( 2 )^2 - ( _/3 )^2
( x = 2+_/3 )
x-1/x = 4 - 3
x-1/x = 1

.:. The value of x-1/x is 1 .