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cho a,b,c>0 thỏa mãn a+b+c=2016
Tìm GTNN P=\(\frac{2a+3b+3c+1}{2015+a}+\frac{3a+2b+3c}{2016+b}+\frac{3a+3b+2c-1}{2017+c}\)
Cho a,b,c>0 thỏa mãn a+b+c=2016
Tìm GTNN P=\(\frac{2a+3b+3c-1}{2015+a}+\frac{3a+2b+3c}{2016+b}+\frac{3a+3b+2c+1}{2017+c}\)
13 tháng 1 2019 lúc 11:08
giúp tớ bài này nha mn . làm 1 trong 2 bài cx đc. cả thì càng tốt
1. cho các số thực dương a,b,c thỏa mãn : a+b+c = 2016
Tìm GTNN của P = \(\frac{2a+3b+3c+1}{2015+a}+\frac{3a+2b+3c}{2016+b}+\frac{3a+3b+2c-1}{2017+c}\)
2. cho x,y > 0 . CMR : \(\frac{x^2}{y^2}+\frac{y^2}{x^2}+4\ge3.\left(\frac{x}{y}+\frac{y}{x}\right)\)
Cho a,b,c>0 CMR:\(\frac{a}{3a^2+2b^2+c^2}+\frac{b}{3b^2+2c^2+a^2}+\frac{c}{3c^2+2a^2+b^2}\le\frac{1}{6}\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)
cho a,b,c >0
CMR:\(\frac{a}{3a^2+2b^2+c^2}+\frac{b}{3b^2+2c^2+a^2}+\frac{c}{3c^2+2a^2+b^2}\le\frac{1}{6}\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)
a) Cho a,b,c>0. chứng minh rằng:\(\frac{a}{3a^2+2b^2+c^2}+\frac{b}{3b^2+2c^2+a^2}+\frac{c}{3c^2+2a^2+b^2}\le\frac{1}{6}\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)
\(\frac{a}{3a^2+2b^2+c^2}+\frac{b}{3b^2+2c^2+a^2}+\frac{c}{3c^2+2a^2+b^2}\le\frac{1}{6}\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)
Cho a,b,c > 0
Chung minh rang : \(\frac{\left(2b+3c\right)^2}{a}+\frac{\left(2c+3a\right)^2}{b}+\frac{\left(2a+3b\right)^2}{c}\ge25\left(a+b+c\right)\)
Cho a, b, c 0. Chứng minh: a)frac{1}{2a+3b+3c} +frac{1}{2b+3c+3a} +frac{1}{2c+3a+3b} le frac{1}{4} (frac{1}{a+b} +frac{1}{b+c} +frac{1}{c+a} ) b)frac{1}{a+2b+3c} +frac{1}{b+2c+3a} +frac{1}{c+2a+3b} le frac{1}{2} (frac{1}{a+2c} +frac{1}{b+2a} +frac{1}{c+2b} )
Đọc tiếp
Cho a, b, c >0. Chứng minh:
a)\(\frac{1}{2a+3b+3c}\) +\(\frac{1}{2b+3c+3a}\) +\(\frac{1}{2c+3a+3b}\) \(\le\) \(\frac{1}{4}\) (\(\frac{1}{a+b}\) +\(\frac{1}{b+c}\) +\(\frac{1}{c+a}\) )
b)\(\frac{1}{a+2b+3c}\) +\(\frac{1}{b+2c+3a}\) +\(\frac{1}{c+2a+3b}\) \(\le\) \(\frac{1}{2}\) (\(\frac{1}{a+2c}\) +\(\frac{1}{b+2a}\) +\(\frac{1}{c+2b}\) )