(本小題滿分13分)
設(shè)

的BC邊上的高AD=BC,a,b,c分別是內(nèi)角A,B,C的對邊。
(1)求

的最小值及取得最小值時

的值;
(2)把

表示為

的形式,判斷

能否等于

?并說明理由。
解:(1)

+


,當且僅當

=



時,即三角形是等腰三角形時,
取得最小值2;
此時

,

…………………………5分
(2)


,

,

+

…………………………9分

,其中

,當且僅當

,即

時,

+

取得

。因為△ABC的BC邊上的高AD=BC,
所以

同時成立,所以a是最小的邊,

,所以

。
因為

,所以

+

可以取到

…………………13分
練習冊系列答案
相關(guān)習題
科目:高中數(shù)學
來源:不詳
題型:單選題

的三內(nèi)角

所對邊的長分別為

設(shè)向量

,

,若

,則角

的大小為( )
查看答案和解析>>
科目:高中數(shù)學
來源:不詳
題型:單選題
在

中,角A、B、C的對邊分別為

、

、

,若

,則B=( )
A.

B.

C.

或

D.

或

查看答案和解析>>
科目:高中數(shù)學
來源:不詳
題型:單選題
若△ABC的內(nèi)角A、B、C所對的邊a、b、c,若角A、B、C依次成等差數(shù)列,且

,則△ABC的面積為
A、

B、

C、

D、
查看答案和解析>>
科目:高中數(shù)學
來源:不詳
題型:解答題
(本小題滿分10分)
已知

的面積是30,內(nèi)角


、

、

所對邊長分別為

、

、

,

.
(1)求

;(2)若

,求

的值.
查看答案和解析>>
科目:高中數(shù)學
來源:不詳
題型:填空題
在△
ABC中,
AB=5,
BC=7,
AC=8,則

=
..
查看答案和解析>>
科目:高中數(shù)學
來源:不詳
題型:填空題
已知數(shù)列

的前

項和為

某三角形三邊之比為

,則該三角形最大角為
■ .
查看答案和解析>>