Question

若x=

3 -1

3 +1

，y=

3 +1

3 -1

，求

x2+y2+2

的值．

Answer 1

分析：观察发现：先化简x，y的值，再计算x，y的和与积．

解答：解：因为x=

3 -1

3 +1

，y=

3 +1

3 -1

所以x+y=

3 -1

3 +1

+

3 +1

3 -1

=

( 3 -1)2+( 3 +1)2

( 3 +1)( 3 -1)

=

4-2 3 +4+2 3

( 3 )2-1

=4．
x•y=

3 -1

3 +1

•

3 +1

3 -1

=1
所以，

x2+y2+2

=

(x+y)2-2xy+2

=

42-2×1+2

=4．

点评：此题主要注意化简x，y的值，再求xy，x+y的值，然后整体代入．