已知x1+x2=3,x1x2=1,求（1）x1分之1+x2分之1的值.（2）x1分之x2+x2分之x1的值.（3）求（x2+1）/（x1+1）+(x1+1)/(x2+1)的值
问题描述：
已知x1+x2=3,x1x2=1,求（1）x1分之1+x2分之1的值.
（2）x1分之x2+x2分之x1的值.
（3）求（x2+1）/（x1+1）+(x1+1)/(x2+1)的值
答
x1+x2=3
两边平方得：
x1²+x2²+2x1x2=9
x1²+x2²=9-2=7
（1）x1分之1+x2分之1
=(x1+x2)/(x1x2)
=3/1
=3
（2）x1分之x2+x2分之x1
=(x1²+x2²)/(x1x2)
=7/1
=7
（3）（x2+1）/（x1+1）+(x1+1)/(x2+1)
=[(x2+1)²+(x1+1)²]/[(x1+1)(x2+1)]
=[(x1²+x2²)+2(x1+x2)+2]/[(x1+x2)+x1x2+1]
=(7+6+2)/(3+1+1)
=15/5
=3
答
(1) 1/x1+1/x2=(x1+x2)/(x1x2)=3/1=3(2) x2/x1+x1/x2=(x1^2+x2^2)/(x1x2)=x1^2+x2^2+2x1x2-2x1x2=(x1+x2)^2-2=9-2=7(3) (x2+1)/(x1+1)+(x1+1)/(x2+1)=[(x2+1)^2+(x1+1)^2]/(x1x2+x1+x2+1)=[x1^2+x2^2+2(x1+x2)+2]/(1...