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
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![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](/uploads/image/z/2518722-18-2.jpg?t=%E5%AE%9E%E6%95%B0x%E3%80%81y%E6%BB%A1%E8%B6%B3x2%2Bxy%2By2%3D2%2C%E8%AE%B0u%3Dx2-xy%2By2%2C%E5%88%99u%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E6%98%AFA.K%EF%BC%9E1+B.-1%EF%BC%9Ck%EF%BC%9C1+C.k%EF%BC%9C-1+D.k%3D1%E9%80%89%E9%A1%B9%E5%8F%91%E9%94%99%E4%BA%86+A.2%2F3%E2%89%A4u%E2%89%A46+B.2%2F3%E2%89%A4u%E2%89%A42+C.1%E2%89%A4u%E2%89%A46+D.1%E2%89%A4u%E2%89%A42)
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