If x > 1 and x ∈ Ν, then which one is correct?

Question: If x > 1 and x ∈ Ν, then which one is correct?
x³ - 1 > x² - x
x³ - 1 < x² - x
x³ - 1 = x² - x
x³ - 1 ≥ x² - x

Solution:
For x > 1 and x ∈ Ν We conduct option test:
Let, x = 2, Which follows the given conditions.

ক) x³ - 1 > x² - x
⇒ 2³ - 1 > 2² - 2
⇒ 8 - 1 > 4 - 2
⇒ 7 > 2
Which is correct.

খ) x³ - 1 < x² - x
⇒ 2³ - 1 < 2² - 2
⇒ 8 - 1 < 4 - 2
⇒ 7 < 2
Which is not correct.

গ) x³ - 1 = x² - x
⇒ 2³ - 1 = 2² - 2
⇒ 8 - 1 = 4 - 2
⇒ 7 = 2
Which is not correct.

ঘ) x³ - 1 ≤ x² - x
⇒ 2³ - 1 ≤ 2² - 2
⇒ 8 - 1 ≤ 4 - 2
⇒ 7 ≤ 2
Which is not correct.

Then, Option ক is correct.