已知a,b,c是正数,且ab+bc+ac=1求证a+b+c大于等于根号3

题目

已知a,b,c是正数,且ab+bc+ac=1求证a+b+c大于等于根号3

答案

(a+b+c)2
=a2+b2+c2+2ab+2bc+2ca
=1/2*（a2+b2+b2+c2+c2+a2)+ab+2bc+2ca]
>=1/2*(2ab+2bc+2ca)+2ab+2bc+2ca
=3ab+3bc+3ca
=3
OK