Question

x1,x2是方程2x²+5x-1=0的两个根,则（x2）/（x1）+（x1）/（x2）=

Answer 1

x1,x2是方程2x²+5x-1=0的两个根
∴x1+x2=-5/2
x1x2=-1/2
x2/x1+x1/x2=(x2²+x1²)/x1x2=[(x1+x2)²-2x1x2]/(x1x2)=(25/4+1)/(-1/2)=-29/2

追问

[(x1+x2)²-2x1x2]/(x1x2）？？？？？这是什么啊

追答

x2²+x1²=x1²+2x1x2+x2²-2x1x2=(x1+x2)²-2x1x2

追问

为什么还要减2X1X2

追答

前面加一个2x1x2 目的是为了配方 多加了2x1x2，就要减去2x1x2

Answer 2

（x2）/（x1）+（x1）/（x2）=x1²+x2²/x1x2=（X1+X2）²-2x1x2/X1x2=(X1+X2/X1X2)-2
X1+X2=-b/a=-5/2 X1X2=c/a=-1/2
（x2）/（x1）+（x1）/（x2）=(X1+X2/X1X2)-2=-5/2/-1/2-2=3