若a+x 2 =2007,b+x 2 =2008,c+x 2 =2009,且abc=24,则 a bc + b ac + c ab

2025-03-07 16:47:17
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回答1:

∵a+x 2 =2007,b+x 2 =2008,c+x 2 =2009,
∴b-a=1,c-b=1,c-a=2,
a
bc
+
b
ac
+
c
ab
-
1
a
-
1
b
-
1
c
=
a
bc
-
1
b
+
b
ac
-
1
c
+
c
ab
-
1
a

=
a-c
bc
+
b-a
ac
+
c-b
ab

=
-2
bc
+
1
ac
+
1
ab

=
-2a+b+c
abc

=
(b-a)+(c-a)
abc

=
1+2
24

=
1
8