@[邰主任](/user/559612)
是
$\dfrac{\sqrt{x^2-x+1}}{x}$
还是
$\sqrt{\dfrac{x^2-x+1}{x}}$
？
by MatrixGroup @ 2022-01-16 22:52:28
@[bilibilitdasc](/user/483824) 如果是下面的直接分离常数然后均值就行了吧
by Ginger_he @ 2022-01-16 22:54:49
上面
by Real_Ikun @ 2022-01-16 22:55:22
$\dfrac{\sqrt{x^2-x+1}}{x}$
$=\sqrt{\dfrac{x^2-x+1}{x^2}}$
$=\sqrt{1-\dfrac{x-1}{x^2}}$
$=\sqrt{1-\dfrac{1}{x+1+\frac{1}{x-1}}}$
$=\sqrt{1-\dfrac{1}{x-1+\frac{1}{x-1}+2}}$
by Ginger_he @ 2022-01-16 23:04:30
@[邰主任](/user/559612) 然后均值
by Ginger_he @ 2022-01-16 23:04:50
就是 $a+b\ge2\sqrt{ab}$
by Ginger_he @ 2022-01-16 23:05:32