已知:a,b,c,d属于R+,求证(b/a+a/b)(d/c+c/d)大于等于4.
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已知:a,b,c,d属于R+,求证(b/a+a/b)(d/c+c/d)大于等于4.
已知:a,b,c,d属于R+,求证(b/a+a/b)(d/c+c/d)大于等于4.
已知:a,b,c,d属于R+,求证(b/a+a/b)(d/c+c/d)大于等于4.
a,b,c,d属于R+
由均值不等式可得
b/a+a/b≥2(当且仅当b/a=a/b,即a=b时 等号成立)
d/c+c/d≥2(当且仅当d/c=c/d,即c=d时 等号成立)
所以,(b/a+a/b)×(d/c+c/d)≥4
当且仅当,a=b且c=d时,等号成立