设

,若对任意的正实数

,都存在以

为三边长的三角形,则实数

的取值范围是
▲ .
因

,若对任意的正实数

,都存在以

为三边长的三角形,则需

,即

,
故

对任意的正实数

恒成立,
因

,

,不妨令

,则

,故

,因

,所以

,又

,因

,所以

,即

的取值范围为

。
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