Các câu hỏi tương tự
Cho a,b,c la cac so duong sao cho a+b+c = 1
Chung minh \(\frac{a^2}{b+c}+\frac{b^2}{a+c}+\frac{c^2}{b+a}>=\frac{1}{2}\)
1. Cho a,b la 2 so duong thoa a+b<=1.chung minh rang \(6b+\frac{1}{3a}+\frac{4}{b}\ge11\).
2. cho a,b,c la cac so nguyen duong sao cho (a-b).(a-c).(b-c)=a+b+c
a. chung minh rang a+b+c chia het cho 2
b. Tim gia tri nho nhat cua M=a+b+c
cho a, b, c la cac so duong thoa man a\(a^2+b^2+c^2=3\) . Chung minh rang : \(\frac{1}{2-a}+\frac{1}{2-b}+\frac{1}{2-c}>=3\)
Cho a,b,c la cac so duong thoa man dieu kien \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1\)
Cmr \(\frac{a^2}{a+bc}+\frac{b^2}{b+ca}+\frac{c^2}{c+ab}\ge\frac{a+b+c}{4}\)
Cho a,b,c la cac so duong thoa man dieu kien \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1\)
Cmr \(\frac{a^2}{a+bc}+\frac{b^2}{b+ca}+\frac{c^2}{c+ab}\ge\frac{a+b+c}{4}\)
cho a,b,c la cac so thuc duong . cm
\(\frac{a}{b^2+c^2}\)\(+\frac{b}{a^2+c^2}+\frac{c}{a^2+b^2}\ge\frac{3\sqrt{3}}{2\sqrt{a^2+b^2+c^2}}\)
Choa,b,c la cac so duong thoa man dieu kien \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1\)
Cmr \(\frac{a^2}{a+bc}+\frac{b^2}{b+ca}+\frac{c^2}{c+ab}\ge\frac{a+b+c}{4}\)
Gia su a, b, c la cac so duong, chung minh rang: \(\sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{c+a}}+\sqrt{\frac{c}{a+b}}>2\)
cho cac so a,b,c duong thoa man ab+bc+ca=1 chung minh : \(p=\frac{2a}{\sqrt{1+a^2}}+\frac{b}{\sqrt{1+b^2}}+\frac{c}{\sqrt{1+c^2}}\)