在△ABC中,角A、B、C的对边分别是a、b、c,若b²+c²=a²+bc
∵pa
=-
ap
，
pb
=
ab
-
ap
，
∴c
ac
+a
pa
+b
pb
=c
ac
-a
ap
+b（
ab
-
ap
）=
0
即c
ac
+b
ab
-（a+b）
ap
=
0
，
∵p是bc边中点，
∴
ap
=
1
2
（
ab
+
ac
），
∴c
ac
+b
ab
-
1
2
（a+b）（
ab
+
ac
）=
0
，
∴c-
1
2
（a+b）=0且b-
1
2
（a+b）=0，
∴a=b=c．
故选a．
^在三角形abc中，a,b,c分别为角a，b，c的
对边
。如果a,b,c成
等差数列
，角b=30度，三角形abc面积为3/2，求b的值
s=acsinb/2=3/2,ac=6,
a
c=2b,a^2
2ac
c^2=4b^2,a^2
c^2-b^2=3b^2-12.
cosb=(a^2
c^2-b^2)/(2ac)=√3/2，
(3b^2-12)/12=√3/2，
b^2=2√3
4，
b=√3
1.
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