共查询到20条相似文献,搜索用时 250 毫秒
1.
2.
3.
《数学教学》2012年第12期的数学问题874为:题目 已知 m,n∈N+,m,n≥2,xi∈R+(i=1,2,…,m),(^m∑i=1)xi=S,n∈N+,求证:(^m∑i=1)^n√xi/S-xi≥.看完此题,笔者不禁想起了文[1]中的不等式:题源1已知a,b,c为正数,求证:√a/(b+c)+√b/(c+a)+√c/(a+b)〉2。 相似文献
4.
5.
6.
7.
8.
题目对任意正实数a、b、c,求证:1〈a/√a^2+b^2+b/√b^2+c^2+c/√c^2+a^2≤3√2/2. 相似文献
9.
文[1]给出了以下不等式的简证与加强,已知a,b〉0,
(1)求证:√a/2b+a+√b/2a+b≤2/√3
(2)求证:√a/2a+b+√b/2b+a≤2/√3 相似文献
10.
2014年全国高中数学联赛A卷加试第一题:设实数a,b,c满足a+b+c=1,abc〉0.求证:ab+bc+ca〈√abc/2+1/4.本文探究这道试题的几种解法,供读者参考。 相似文献
12.
13.
14.
With the help of continued fractions, we plan to list all the elements of the set Q△ = {aX2 + bXY + cY2 : a,b, c ∈Z, b2 - 4ac = △ with 0 ≤ b 〈 √△}of quasi-reduced quadratic forms of fundamental discriminant △. As a matter of fact, we show that for each reduced quadratic form f = aX2 + bXY + cY2 = (a, b, c) of discriminant △〉0(and of sign σ(f) equal to the sign of a), the quadratic forms associated with f and defined by {〈a+bu+cu2,b+2cu.c〉},with 1≤σ(f)u≤b/2|c| (whenever they exist), 〈c,-b-2cu,a+bu+cu2〉 with b/2|c|≤σ(f)u≤[w(f)]=[b+√△/2|c|], are all different from one another and build a set I(f) whose cardinality is #I(f)={1+[ω(f)],when(2c)|b,[ω(f)],when (2c)|b. If f and g are two different reduced quadratic forms, we show that I(f) ∩ I(g) = Ф. Our main result is that the set Q△ is given by the disjoint union of all I(f) with f running through the set of reduced quadratic forms of discriminant △〉0. This allows us to deduce a formula for #(Q△) involving sums of partial quotients of certain continued fractions. 相似文献
15.
17.
18.
题目 已知a1+a2+a3=4,b1+b2+b3=3,且a1,a2,a3,b1,b2,b3均为正数,试求√a1^2+b1^2+√a2^2+b2^2+√a3^2+b3^2的最小值。 相似文献
19.
In this article, we prove that the double inequality
αP(a,b)+(1-α)Q(a,b)〈M(a,b)〈βP(a,b)+(1-β)Q(a,b)
holds for any a,b 〉 0 with a ≠ b if and only if α≥1/2 and β≤[π(√2 lov (1+√2)-1]/[√2π-2) log (1+√2)]=0.3595…,where M(a, b), Q(a, b), and P(a, b) ave the Neuman-Sandor, quadratic, and first Seiffert means of a and b, respectively. 相似文献
αP(a,b)+(1-α)Q(a,b)〈M(a,b)〈βP(a,b)+(1-β)Q(a,b)
holds for any a,b 〉 0 with a ≠ b if and only if α≥1/2 and β≤[π(√2 lov (1+√2)-1]/[√2π-2) log (1+√2)]=0.3595…,where M(a, b), Q(a, b), and P(a, b) ave the Neuman-Sandor, quadratic, and first Seiffert means of a and b, respectively. 相似文献
20.
瓦西列夫不等式:
设n,b,c〉0,n+b+c=1,则a^2+b/b+c+b^2+c/c+a+c^2+a/a+b≥2. 相似文献