问题 填空题
已知x+y=6,xy=-2,则
1
x2
+
1
y2
=______.
答案

1
x2
+
1
y2
=
x2+y2
x2y2
=
(x+y)2-2xy
(xy)2

∵x+y=6,xy=-2,

∴原式=

62-2×(-2)
(-2)2
=
36+4
4
=10

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