Solution:

Finding x ^ 2:

We can simplify the given expression by rationalizing the denominator. To do this, we multiply both the numerator and denominator by the conjugate of the denominator, which is (sqrt(3) + sqrt(2)).

So, x = (sqrt(3) sqrt(2))/(sqrt(3) - sqrt(2))
= [(sqrt(3) sqrt(2))(sqrt(3) + sqrt(2))] / [(sqrt(3) - sqrt(2))(sqrt(3) + sqrt(2))]
= (3 + 2sqrt(6) + 2) / (3 - 2)
= 5 + 2sqrt(6)

Now, we can find x ^ 2 by squaring both sides of the equation:

x ^ 2 = (5 + 2sqrt(6))^2
= 25 + 20sqrt(6) + 24
= 49 + 20sqrt(6)

Therefore, x ^ 2 = 49 + 20sqrt(6).

Finding 1/(x ^ 2):

To find 1/(x ^ 2), we can use the value of x ^ 2 that we just found:

1/(x ^ 2) = 1 / (49 + 20sqrt(6))

To rationalize the denominator, we can multiply both the numerator and denominator by the conjugate of the denominator, which is (49 - 20sqrt(6)):

1/(x ^ 2) = (1 / (49 + 20sqrt(6))) * ((49 - 20sqrt(6)) / (49 - 20sqrt(6)))
= (49 - 20sqrt(6)) / (2404 - 2000)
= (49 - 20sqrt(6)) / 404

Therefore, 1/(x ^ 2) = (49 - 20sqrt(6)) / 404.