问题
填空题
已知a，b，c是非零有理数，且满足ab2=
|
答案
∵ab2=
-b，c a
∴a2b2=c-ab，a2b2-c=-ab，c-a2b2=ab．
∴
-a2b2 c2
+2 c
+1 a2b2
-2ab c2
=（2 abc
-ab c
）2+1 ab
-2a2b2 abc2
=（2c abc2
）2+a2b2-c abc
=（2(a2b2-c) abc2
）2+-ab abc
=-2ab abc2
-1 c2
=-2 c2
，1 c2
-2 ab
=2ab c
=2c-2a2b2 abc
=2ab abc
，2 c
(
-a2b2 c2
+2 c
+1 a2b2
-2ab c2
)÷(2 abc
-2 ab
)÷2ab c
=-101 c
÷1 c2
÷2 c
=-101 c
•1 c2
•c 2
=-c 101
．1 202
故答案为-
．1 202