实数x、y满足x2+xy+y2=2,记u=x2-xy+y2,则u的取值范围是A.K＞1 B.-1＜k＜1 C.k＜-1 D.k=1选项发错了 A.2/3≤u≤6 B.2/3≤u≤2 C.1≤u≤6 D.1≤u≤2

实数x、y满足x2+xy+y2=2,记u=x2-xy+y2,则u的取值范围是A.K＞1 B.-1＜k＜1 C.k＜-1 D.k=1选项发错了 A.2/3≤u≤6 B.2/3≤u≤2 C.1≤u≤6 D.1≤u≤2
实数x、y满足x2+xy+y2=2,记u=x2-xy+y2,则u的取值范围是
A.K＞1 B.-1＜k＜1 C.k＜-1 D.k=1
选项发错了 A.2/3≤u≤6 B.2/3≤u≤2 C.1≤u≤6 D.1≤u≤2

实数x、y满足x2+xy+y2=2,记u=x2-xy+y2,则u的取值范围是A.K＞1 B.-1＜k＜1 C.k＜-1 D.k=1选项发错了 A.2/3≤u≤6 B.2/3≤u≤2 C.1≤u≤6 D.1≤u≤2
x2+xy+y2=(x+y)2-xy=2,所以(x+y)2=2+xy.
2|xy|+xy≤x2+xy+y2=2,所以0≤xy≤2/3.或者-2≤xy≤0
u=x2-xy+y2=(x+y)2-3xy=2-2xy,
0≤xy≤2/3时,2/3≤u≤2 ,
-2≤xy≤0时,2≤u≤6
因此选A

假设X，Y，Z都是正数 因为X2+Y2+Z2=1，所以（X2+Y2）+（X2+Z2）有最小值-1 XY+YZ+ZX的取值范围是[-1，1]。 (x+y)2+(y+z)

当xy>0时，x^2+y^2>=2xy，可推出xy<2/3，当xy<0时，x^2+y^2>=-2xy，推出xy>=-2，即-2<=xy<=2/3又x^2+y^2=u+xy代入x^2+y^2+2xy=2得u+2xy=2所以2/3<=u<=6