查看“︁绝对值不等式”︁的源代码

'''绝对值不等式'''是一个关于[[绝对值]]的不等式，在一般的情况下指代的是下面这组不等式。当<math>a,b</math>为实数时，
<center><math>\mid \shortmid a \shortmid-\shortmid b\shortmid\mid \leqslant \mid a\pm b \mid  \leqslant \mid a \mid +\mid b \mid</math>  </center>
等号成立的充分必要条件：
:{| class="wikitable" cellpadding="10"
|-
|<math>\mid \shortmid a \shortmid-\shortmid b\shortmid\mid = \mid a + b \mid</math>
|<math>\Leftrightarrow a \cdot b \leqslant 0</math>
|-
|<math>\mid \shortmid a \shortmid-\shortmid b\shortmid\mid = \mid a - b \mid</math>
|<math>\Leftrightarrow a \cdot b \geqslant 0</math>
|-
|<math>\mid a + b \mid = \mid a \mid +\mid b \mid</math>
|<math>\Leftrightarrow a \cdot b \geqslant 0</math>
|-
|<math>\mid a - b \mid = \mid a \mid +\mid b \mid</math>
|<math>\Leftrightarrow a \cdot b \leqslant 0</math>
|}

{{Math-stub}}
[[Category:代数不等式]]