Question

If x = root13 + 2root3, find the value of x-1/x

Answer 1

Step-by-step explanation:

Given, x = √13 + 2√3

So 1/x = 1/(√13 + 2√3)

Now 1/x needs to be rationalised as to make root numbers disappear.

For doing that, we multiply numerator and denominator both by its conjugate. For √13+2√3, it's conjugate is √13 - 2√3

So,

1/x =

1/(√13+2√3)*(√13 - 2√3)/(√13 -2√3)

= √13 - 2√3 / 13 - 12

= √13 - 2√3

Now it's easier to solve x - 1/x

x - 1/x

= √13 + 2√3 - √13 + 2√3

= 4√3

Answer 2

Answer:

4√3

Step-by-step explanation:

x=√13+2√3

1/x=1/√13+2√3*√13-2√3/13-2√3

=√13-2√3/(√13)²-(2√3)²

=√13-2√3/13-12

=√13-2√3

x-1/x=√13+2√3-(√13-2√3)

=√13+2√3-√13+2√3

=2√3+2√3

=4√3