Given:
x = 3 - 2√2

To find the value of x^2 - 1/x, we need to substitute the value of x and simplify the expression.

Solution:

Step 1: Substitute the value of x into the expression.
x^2 - 1/x = (3 - 2√2)^2 - 1/(3 - 2√2)

Step 2: Simplify the expression using the formula (a - b)^2 = a^2 - 2ab + b^2.
x^2 - 1/x = (3^2 - 2 * 3 * 2√2 + (2√2)^2) - 1/(3 - 2√2)

Step 3: Simplify further.
x^2 - 1/x = (9 - 12√2 + 8) - 1/(3 - 2√2)
= (17 - 12√2) - 1/(3 - 2√2)

Step 4: Rationalize the denominator.
To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator.
x^2 - 1/x = (17 - 12√2) * (3 + 2√2) / ((3 - 2√2) * (3 + 2√2))
= (17 - 12√2) * (3 + 2√2) / (3^2 - (2√2)^2)
= (17 - 12√2) * (3 + 2√2) / (9 - 8 * 2)
= (17 - 12√2) * (3 + 2√2) / (9 - 16)
= (17 - 12√2) * (3 + 2√2) / (-7)

Step 5: Simplify the expression.
x^2 - 1/x = - (17 - 12√2) * (3 + 2√2) / 7
= - (51 + 34√2 - 36√2 - 48) / 7
= - (3 - 2√2) / 7
= - x / 7

Therefore, the value of x^2 - 1/x is - x / 7.

Conclusion:
x^2 - 1/x = - x / 7