已知实数x,y满足3小于等于xy^2小于等于8,4小于等于x^2/y小于等于9,则x^3/y^4的取值范围
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3<=xy^2<=8 4<=x^2/y<=9
所以x>0 y>0
9<=x^2y^4<=64 1/9<=y/x^2<=1/4
1<=y^5<=16
所以1<=y<=16^(1/5) 4<=x^2/y<=9
1<=y^2<=16^(2/5) 4<=x^2<=9*16^(1/5)
16^(-2/5)<=1/y^2<=1
3*16^(-2/5)<=x<=8 2<=x<=3*4^(1/5)
所以2<=x<=3*4^(1/5) 16^(-2/5)<=1/y^2<=1
8<=x^3<=27*4^(3/5) 16^(-4/5)<=1/y^4<=1
所以2^(-1/5)<=x^3/y^4<=27*4^(3/5)
所以x>0 y>0
9<=x^2y^4<=64 1/9<=y/x^2<=1/4
1<=y^5<=16
所以1<=y<=16^(1/5) 4<=x^2/y<=9
1<=y^2<=16^(2/5) 4<=x^2<=9*16^(1/5)
16^(-2/5)<=1/y^2<=1
3*16^(-2/5)<=x<=8 2<=x<=3*4^(1/5)
所以2<=x<=3*4^(1/5) 16^(-2/5)<=1/y^2<=1
8<=x^3<=27*4^(3/5) 16^(-4/5)<=1/y^4<=1
所以2^(-1/5)<=x^3/y^4<=27*4^(3/5)
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