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在文[1]中,华罗庚留给读者证明的两个不等式为:6(|ad-bc|)~(1/2)≤2(a~2+c~2)~(1/2)+(a~2+c~2+3(b~2+d~2)-2 3~(1/2)(ab+cd))~(1/2) +(a~2+c~2+3(b~2+d~2)+2 3~(1/2)(ab+cd))①16|ad-bc|~3≤(a~2+c~2){[a~2+c~2+3(~2+d~2)]~2-12(ab+cd)~2}②在文[2]中,该文作者通过构造引理:“设x≥u≥0,则16(x-u)~(3/2)≤(1+3x)~2-12u”证明了上述两个不等式.但遗憾的是,证明过程相当长,且需要
In the paper [1], two inequalities proved to be proved by Hua Luogeng are: (| ad-bc |) ~ (1/2) ≤2 (a ~ 2 + c ~ 2) (a ~ 2 + c ~ 2 + 3 (b ~ 2 + d ~ 2) -2 3 ~ (1/2) (ab + cd)) ~ (1/2) + (a ~ 2 + c ~ 2 + 3 b ~ 2 + d ~ 2 + 2 3 ~ (1/2) (ab + cd)) ①16 | ad-bc | ~ 3 ≦ (a ~ 2 + c ~ 2) {[a ~ 2 + c ~ 2 + 3 (~ 2 + d ~ 2)] ~ 2-12 (ab + cd) ~ 2} In the paper [2], the author of this paper constructs lemma: “Let x≥u≥0, Then 16 (xu) ~ (3/2) ≤ (1 + 3x) ~ 2-12u ”prove the above two inequalities. But unfortunately, the proof process is quite long and needs