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設x,y為實數,x>1,y>1,且滿足2[logx(y)]-2[logy(x)]+3=0,求x^2-4y^2的最小值? 解法:x>1,y>1,=>logx (y)>0且[logy (x)]>0 假設a=logx (y)>0則logy (x)=1/a 2[logx(y)]-2[logy(x)]＋3=0 <=>2a-2[1/a]＋3=0 <=>2a2＋3a-2=0 <=>(2a-1)(a＋2)=0 =>a=1/2 =>logx (y)=1/2 =>y2=x =>x2-4y2 =x2-4x =(x-2)2 - 4 x=2時，上式有最小值- 4 (此題為某大學第二階段甄試題目)