灵朦
幼苗
共回答了981个问题 举报
证0f(x2)-f(x1)=x2^2-x1^2+a^2(1/x2-1/x1)
=(x2+x1)(x2-x1)+a^2(x1-x2)/x1x2
=(x2-x1)(x2+x1-a^2/x1x2)
=(x2-x1)(x2^2+x1x2-a^2)/x1x2
x2^2+x1x2-a^2=-(a^2-x2)^2+x1x2-ax2
-(a^2-x2)^2<0
x1x2-ax2<0
x2^2+x1x2-a^2<0
(x2-x1)>0
(x2-x1)(x2^2+x1x2-a^2)/x1x2<0
f(x2)-f(x1)<0
1年前
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