实数x、y满足x2+xy+y2=2,记u=x2-xy+y2,则u的取值范围是

题目

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

答案

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