найдите наибольшее значение выражения А. При каких значениях х и у оно достигается
1)A=6y-4x-x2-y2
2)A=10x-2y-x2-y2+3
3)A=4x+5-3x2-y2-2xy
1)A=6y-4x-x2-y2
2)A=10x-2y-x2-y2+3
3)A=4x+5-3x2-y2-2xy
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1) A = -(x^2 + 4x + 4) + 4 - (y^2 - 6y + 9) + 9 = -(x+2)^2 - (y-3)^2 + 13Максимум равен 13 при x = -2; y = 3
2) A = -(x^2 - 10x + 25) + 25 - (y^2 + 2y + 1) + 1 + 3 = -(x-5)^2 - (y+1)^2 + 29
Максимум равен 29 при x = 5; y = -1
3) A = -3x^2 - 2xy - y^2 + 4x + 5 = -(x^2 + 2xy + y^2) - 2x^2 + 4x + 5 =
= -(x^2 + 2xy + y^2) - 2(x^2 - 2x + 1) + 2 + 5 = -(x+y)^2 - 2(x-1)^2 + 7
Максимум равен 7 при x = 1; y = -x = -1