If x and y are all real numbers, and a = xsquare - 2Y + 1, B = ysquare - 2x + 2, it is proved that at least one of a and B is greater than 0

If x and y are all real numbers, and a = xsquare - 2Y + 1, B = ysquare - 2x + 2, it is proved that at least one of a and B is greater than 0

Suppose that a and B are less than or equal to 0, then a + B ≤ 0
X squared - 2Y + 1 ≤ 0 and
Y square - 2x + 2 ≤ 0
Add to get x ^ 2-2x + 1 + y ^ 2-2y + 2 = (x-1) ^ 2 + (Y-1) ^ 2 + 1 ≥ 1, which contradicts the hypothesis, so the hypothesis is not tenable, in other words, at least one of a and B is greater than 0