若正数a,b满足a2/(a4+a2+1)=1/24, b3/(b6+b3+1)=1/19,则ab/(a2+a+1)(b2+b+1)=
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若正数a,b满足a2/(a4+a2+1)=1/24, b3/(b6+b3+1)=1/19,则ab/(a2+a+1)(b2+b+1)=
若正数a,b满足a2/(a4+a2+1)=1/24, b3/(b6+b3+1)=1/19,则ab/(a2+a+1)(b2+b+1)=
若正数a,b满足a2/(a4+a2+1)=1/24, b3/(b6+b3+1)=1/19,则ab/(a2+a+1)(b2+b+1)=
a² /(a⁴+a²+1)=1/24
(a⁴+a²+1)/a²=24
a²+1+1/a²=24
(a+1/a)²-1=24
(a+1/a)²=25
a是正数
a+1/a=5
b^3/(b^6+b^3+1)=1/19
(b^6+b^3+1)/b^3=19
b^3+1+1/b^3=19
(b+1/b)^3-3b-3/b+1=19
(b+1/b)^3-3(b+1/b)-18=0
(b+1/b)^3-3(b+1/b)^2+3(b+1/b)^2-3(b+1/b)-18=0
(b+1/b)^2(b+1/b-3)+3[(b+1/b)^-(b+1/b)-6]=0
(b+1/b)^2(b+1/b-3)+3(b+1/b-3)(b+1/b+2)=0
(b+1/b-3)[(b+1/b)^2+3(b+1/b+2)]=0
(b+1/b)^2+3(b+1/b+2)
=(b+1/b)^2+3(b+1/b)+6
=(b+1/b+3/2)^2-9/4+6>0
所以b+1/b-3=0
b+1/b=3
(a²+a+1)(b²+b+1)/ab
=(a+1+1/a)(b+1+1/b)
=(5+1)(3+1)
=24
题目不对吧
b这里错了
若正数a,b满足a2/(a4+a2+1)=1/24, b3/(b6+b3+1)=1/19,则ab/(a2+a+1)(b2+b+1)=
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