Ах + by = 5
ax + 3y = 7 - b
X = 4
y = - 2
Решение
4а - 2b = 5
4a - 6b = 7 - b
- 4a + 6b = b - 7
4b = b - 2
3b = - 2
b = - 2/3
4a - 2( - 2/3 ) = 5
4a = 5 + ( 4/3 )
4a = 19/3
a = 19/12
a = 1 7/12
Ответ ( 1 7/12 ; - 2/3 )
F(x)=3+4x-x²
F'(x)=4-2x=0
x*=2
F(x*)=3+4•2-2²=3+8-4=7
Точка экстремума (2;7)
x+y+z=4
2xy-z^2=16
z=4-(x+y)
2xy-16+8(x+y)-(x+y)^2=16
2xy-16+8(x+y)-x^2-2xy-y^2=16
-x^2-y^2+8(x+y)=32
(-x^2+8x-16)+(-y^2+8y-16)=0
-(x-4)^2-(y-4)^2=0
-(x-4)^2=(y-4)^2
x-4=0
y-4=0
x=4
y=4
z=-4
x+y+2z=0