题目内容
已知a,b是正实数,求证:a | ||
|
b | ||
|
a |
b |
分析:由a,b是正实数,(
+
) - (
+
)=
≥0,即可证得结论.
a | ||
|
b | ||
|
a |
b |
(
| ||||||||
|
解答:证明:∵a,b是正实数,(
+
) - (
+
)=
=
=
≥0,
∴
+
≥
+
成立.
a | ||
|
b | ||
|
a |
b |
a
| ||||||||
|
=
(
| ||||
|
(
| ||||||||
|
∴
a | ||
|
b | ||
|
a |
b |
点评:本题考查用作差比较法证明不等式,把差式化成因式乘积的形式,是解题的关键.
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