Question

已知x=

2 -1

2 +1

， y=

2 +1

2 -1

，则x²-xy+y²=______．

Answer 1

x=

2 -1

2 +1

=（

2

-1）²=3-2

2

；
y=

2 +1

2 -1

=（

2

+1）²=3+2

2

．
x²-xy+y²
=（3-2

2

）²-

2 -1

2 +1

•

2 +1

2 -1

+（3+2

2

）²
=17-12

2

-1+17+12

2

=34-1
=33．