Question

已知有理数a,b,c,满足abc>0,设x=｜a｜/a+｜b｜/b+｜c｜/c,y=a(1/b+1/c)+b(1/a+1

Answer 1

由abc>0,

得a,b,c三个数的符号三正,两负一正,

若三个正：x=｜a｜/a+｜b｜/b+｜c｜/c=3

若两个负一正：x=｜a｜/a+｜b｜/b+｜c｜/c=-1

y=a(1/b+1/c)+b(1/a+1/c)+c(1/a+1/b)

=a/b+a/c+b/a+b/c+c/a+c/b

=(a+b)/c+(b+c)/a+(a+c)/b

=-3

x+2y+3xy

=3-6-27

=-30

或

x+2y+3xy

=-1-6+9

=2