问题
解答题
已知实数a,b分别满足3a4+2a2-4=0和b4+b2-3=0,求
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答案
由3a4+2a2-4=0,得a2=
,即a2=-2± 4-4×3×(-4) 2×3
,-1± 13 3
∵a2≥0,
∴a2=
①-1+ 13 3
由b4+b2-3=0,得b2=
,即b2=-1± 1-4×1×(-3) 2×1
;-1± 13 2
又∵b2≥0,
∴b2=
②-1+ 13 2
∴
+b44 a4
=
+(4 (
)2-1+ 13 3
)2-1+ 13 2
=
+18 7- 13 7- 13 2
=
+18×(7+
)13 (7-
)(7+13
)13 7- 13 2
=
+7+ 13 2 7- 13 2
=7,
即
+b4=7.4 a4