已知a,b,c属于R+ 求证:(a/b+b/c+c/a)(b/a+a/c+c/b)大于等于9
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已知a,b,c属于R+ 求证:(a/b+b/c+c/a)(b/a+a/c+c/b)大于等于9
已知a,b,c属于R+ 求证:(a/b+b/c+c/a)(b/a+a/c+c/b)大于等于9
已知a,b,c属于R+ 求证:(a/b+b/c+c/a)(b/a+a/c+c/b)大于等于9
思路:欲证此题,必须借助常用的不等式:a+b+c≥3*三次根号下abc,等号当且仅当a=b=c时成立.
证明:
(a/b+b/c+c/a)(b/a+a/c+c/b)
≥3*三次根号(a/b*b/c*c/a)*3*三次根号(b/a*a/c*c/b)
=9
等号当且仅当a=b=c时成立.
a^3+b^3+c^3≥3abc,或者令a^3=x,b^3=y,c^3=z,则有
x+y+z≥3*三次根号下(xyz),相关证明可参考: