实数xy满足x+y-2≥0,x+3y-6≤0,x-2≤0则x^2+y^2+2x+2y的最小值

证明x、y大于等于0∵x+y-2≥0,x+3y-6≤0∴2-y≤x≤6-3y,2-y≤6-3y,y≤2∵x-2≤0,x+y-2≥0∴2-y≤x≤2,y≥0∵0≤y≤2,x+y-2≥0∴0≤x≤2证明x+y与xy的取值范围∵x+y-2≥0,x+y≥2又∵x+y≥2√xy∴2√xy≤2,xy≤1x²...