若方程x²-3x-1=0的两根分别是x1和x2.则1/x1²+1/x2²=
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![若方程x²-3x-1=0的两根分别是x1和x2.则1/x1²+1/x2²=](/uploads/image/z/2082673-1-3.jpg?t=%E8%8B%A5%E6%96%B9%E7%A8%8Bx%26%23178%3B-3x-1%3D0%E7%9A%84%E4%B8%A4%E6%A0%B9%E5%88%86%E5%88%AB%E6%98%AFx1%E5%92%8Cx2.%E5%88%991%EF%BC%8Fx1%26%23178%3B%2B1%EF%BC%8Fx2%26%23178%3B%3D)
若方程x²-3x-1=0的两根分别是x1和x2.则1/x1²+1/x2²=
若方程x²-3x-1=0的两根分别是x1和x2.则1/x1²+1/x2²=
若方程x²-3x-1=0的两根分别是x1和x2.则1/x1²+1/x2²=
方程x²-3x-1=0的两根分别是x1和x2
∴x1+x2=3
x1x2=-1
1/x1²+1/x2²
=(x1²+x2²)/(x1x2)²
=[(x1+x2)²-2x1x2]/(x1x2)²
=(9+2)/1
=11
x1+x2=3 (1)
x1x2=-1 (2)
(1)/(2)
1/x1+1/x2=-3
两边平方
1/x1²+2/x1x2+1/x2²=9
1/x1²-2+1/x2²=9
1/x1²+1/x2²=11