Question

1.已知X,Y,Z为实数,且X+Y+Z=5,XY+YZ+ZX=3,则Z得取值范围为?

Answer 1

1,x=5-y-z,xy=5y-y^2-yz

xy+yz+zx=xy+z(x+y)=5y-y^2-yz +z(5-z)

=-y^2+(5-z)y+z(5-z)=3

y^2-(5-z)y+3+z^2-5z=0

y是实数,所以:判别式:(5-z)^2-4(3+z^2-5z)=-3z^2+10z+13≥0,

3z^2-10z-13=(3z-13)(z+1)≤0,

-1≤z≤13/3

2,作B点关于X轴的对称点B'(5,2),连接AB',并延长至与X轴的交点,即为P的坐标

2/3=(x-5)/(x-1),x=13,点P坐标(13,0)

3,x2x3...x2007=1/x1,x1-1/x1=1,

x1^2-x1-1=0,设其两根为a,b,那么a+b=1,ab=-1

b/a=b^2/ab=-b^2=-(b+1)=-(3+√5)/2

a/b=a^2/ab=-a^2=-(a+1)=-(3-√5)/2

.

a2006=1 或 -(3+√5)/2或-(3-√5)/2