It is known that real numbers a, B and C satisfy the following conditions: a = x squared - 2Y + π / 2, B = y squared - 2x + π / 3, C = Z squared - 2x + π / 6 Verification: at least one of a, B, C is greater than 0 | Math enthusiast | Mathematical art

It is known that real numbers a, B and C satisfy the following conditions: a = x squared - 2Y + π / 2, B = y squared - 2x + π / 3, C = Z squared - 2x + π / 6 Verification: at least one of a, B, C is greater than 0

Suppose that a, B, C are less than or equal to 0A + B + C = x ^ 2-2y + π / 2 + y ^ 2-2z + π / 3 + Z ^ 2-2x + π / 6 = (x ^ 2-2x) + (y ^ 2-2y) + (Z ^ 2-2z) + π = (x-1) ^ 2 + (Y-1) ^ 2 + (Z-1) ^ 2 + π - 3 > 0, which is contradictory to the assumption that a, B, C are less than or equal to 0, so the assumption is wrong, so at least one of a, B, C is greater than 0

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