Để chứng minh rằng P > 1/3, ta sẽ sử dụng phương pháp giả sử ngược.

Giả sử P ≤ 1/3, tức là căn(X-2)/cănX ≤ 1/3.

Bình phương cả hai vế ta được: (căn(X-2)/cănX)² ≤ (1/3)².

Simplifying the right side, we have: (căn(X-2)/cănX)² ≤ 1/9.

Taking the square root of both sides, we have: căn(X-2)/cănX ≤ 1/3.

Multiplying both sides by cănX, we have: căn(X-2) ≤ cănX/3.

Squaring both sides, we have: X-2 ≤ X²/9.

Multiplying both sides by 9, we have: 9X - 18 ≤ X².

Rearranging the equation, we have: X² - 9X + 18 ≥ 0.

Factoring the quadratic equation, we have: (X-3)(X-6) ≥ 0.

This inequality holds true when X ≤ 3 or X ≥ 6.

However, since X > 2 (as căn(X-2) is defined), we can conclude that X ≥ 6.

But this contradicts our initial assumption that P ≤ 1/3.

Therefore, our assumption is false and P > 1/3.