由于a>0
a^2+c^2=2ab>0
=>b>0
bc>a²=>c>0
a^2-2ab+c^2=0
a^2-2ab+b^2+c^2-b^2=0
(a-b)^2=b^2-c^2≥0
=>b^2≥c^2當(dāng)c=b時(shí)等號(hào)成立
如果b=c
那么a^2-2ab+c^2=0
得到a^2-2ac+c^2=0
a=c
這樣a=b=c,與bc>a²矛盾,所以b不等于c
=>b>c
b>c,兩邊同乘以b
b^2>bc>a^2=>b>a
又a^2+c^2=2ab>2a^2
=>c^2>a^2=>c>a
=>b>c>a