若x1,x2是方程2x的平方-4x-5=0的两根,求下列各式的值
问题描述:
若x1,x2是方程2x的平方-4x-5=0的两根,求下列各式的值
(1)x1的平方+x2的平方
(2)x2/x1+x1/x2
(3)(x1-x2)的平方
(4)(x1-1/x2)(x2-1/x2)
要有过程!希望快些!明天就得交!
答
x1+x2=2
x1x2=-5/2
所以
x1²+x2²
=(x1+x2)²-2x1x2
=4+5
=9
x2/x1+x1/x2
=(x2²+x1²)/x1x2
=9/(-5/2)
=-18/5
(x1-x2)
=x1²+x2²-2x1x2
=9+5
=14
(x1-1/x1)(x2-1/x2)
=x1x2-x1/x2-x2/x1+1/x1x2
=x1x2+1/x1x2-(x2/x1+x1/x2)
=-5/2-2/5+18/5
=7/10