Question

已知x1+x2=3,x1x2=1,求（x2+1）/（x1+1）+(x1+1)/(x2+1)的值

Answer 1

（x2+1）/（x1+1）+(x1+1)/(x2+1)

=（x2+x1x2）/（x1+x1x2）+(x1+x1x2)/(x2+x1x2)

=x2（x1+x2）/[x1（x1+x2）]+x1（x1+x2）/[x2（x1+x2）]

=x2/x1+x1/x2

=(x2^+x1^2)/（x1x2）

=[(x1+x2)^2-2x1x2]/(x1x2)

=9-2

=7