若xy=2,求1/(4x^2)+1/(9y^2)的最值

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若xy=2,求1/(4x^2)+1/(9y^2)的最值
若xy=2,求1/(4x^2)+1/(9y^2)的最值

若xy=2,求1/(4x^2)+1/(9y^2)的最值
∵xy=2, ∴Y=2/X
1/(4x^2)+1/(9y^2)=1/4X²+1/(9(2/X)²)=1/4(1/X²+X²/9)
由 a²+b²≥2ab 得 1/X²+X²/9 ≥ 2×(1/x )( x/3 ) ∴ 1/X²+X²/9 ≥ 6
1/(4x^2)+1/(9y^2) ≥ 6/4
1/(4x^2)+1/(9y^2)的最小值是3/2