Question

求一元二次方程x²-x-1=0的根x1,x2

Answer 1

一元二次方程x²-x-1=0的根x1,x2

x1+x2=1,x1x2=-1

x1²+x2² =(x1+x2)²-2x1x2=-+2=3

x1分之1 + x2分之1=(x1+x2)/x1x2=1/(-1)=-1

(x1-x2）²=(x1+x2)²-4x1x2=1+4=5

(x1+1)(x2+1)=x1x2+x1+x2+1=1-1+1=1