用韦达定理:
X1+X2=-b/a =4/1=4
X1*X2=c/a=2/1=2
则1/x1+1/x2=x1+x2/x1*x2=4/2=2
|x1-x2|=(根号下)(x1-x2)^2=(根号下)(x1^2-2*x1*x2+x2^2)=(根号下)(x1+x2)^-4*x1*x2=(根号下)(16-8)=2√2
{x1+1}{x2+1}=x1*x2+x1+x2+1=2+4+1=7
[2] 2x^2-x-4=0的两根为x1+ x2=1/2,x1*x2=-2则1/x1+1/x2=x1+x2/x1*x2=(1/2)/-2=-1/4,(1/x1)*(1/x2)=1/x1*x2=-1/2.
则4x^2+x-2=0