设a,b,c均为正实数,求证1/2a+1/2b+1/2c大于等于1/(b+c)+1/(c+a)+1/(a+b)

来源：学生作业学帮网编辑：学帮网时间：2024/05/05 04:21:53

证明：∵1/x+1/y>-4/(x+y)=(x+y)/(xy)-4/(x+y)
=[(x+y)^2-4xy]/[(xy)(x+y)]
=(x-y)^2/[(xy)(x+y)]
当x>0,y>0时 (x-y)^2/[(xy)(x+y)]>=0
∴1/(4x)+1/(4y)>=1/(x+y)
从而 1/2a+1/2b+1/2c=1/4a+1/4b+1/4b+1/4c+1/4c+1/4a
>=1/(a+b)+1/(b+c)+1/(c+a)
∴1/2a+1/2b+1/2c大于等于1/(b+c)+1/(c+a)+1/(a+b)

设a b c均为正实数求证1/2a+1/2b+1/2C >= 1/(b+c)+1/(c+a)+1/(a+b) 设a,b,c均为正实数,求证：1/2a+1/2b+1/2c》1/(b+c)+1/(c+a)+1/(a+b) 设a,b,c为正实数,求证1／a+1／b+1／c+abc≥2√3 设a,b,c均为正实数,求证:a+1/b,b+1/c,c+1/a中至少有一个不小于2如题~ 设abc为正实数,求证:a+b+c 数学不等式求证题设a,b,c均为正实数,求证（1/2a)+(1/2b)+(1/2c)>=(1/(b+c))+(1/(c+a))+(1/(a+b)) 设a,b,c为正实数,求证1／a3+1／b3+1／c3+abc≥2√3 设a.b.c为正实数,求证：1/a3+1/b3+1/c3+>=2根号3 设a,b,c均为正实数,求证：a/(b+c)+b/(a+c)+c/(a+b)大于等于3/2 数学题在线解答设a,b,c均为正实数,求证1/2a+1/2b+1/2c大于等于1/(b+c)+1/(c+a)+1/(a+b) 设a,b,c均为正实数,求证1/2a+1/2b+1/2c大于等于1/(b+c)+1/(c+a)+1/(a+b) 一道关于不等式的证明题,设a,b,c均为正实数,求证1/2a +1/2b +1/2c>=1/(b+c) +1/(a+c)+ 1/(a+b) 设a,b,c为正实数,求证1/a^3+ 1/b^3+ 1/c^3+ abc>=2根号3 设a.b.c为正实数求证1/a^3+1/b^3+1/c^3+abc>=2√3 设a,b均为正实数,求证:1/aa+1/bb+ab≥2√2 设a、b、c均为正实数,求（a+b+c)[1/(a+b)+1/c]的最小值. 设a,b,c均为实数,求证：1/2a+1/2b+1/2c>=1/(b+c)+1/(a+c)+1/(a+b) 设啊,a,b,c均为实数,求证1/2a/2b/2c≥1/b+c +1/c+a +1/a+b