Các câu hỏi tương tự
Choa,b,c la cac so duong thoa man dieu kien \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1\)
Cmr \(\frac{a^2}{a+bc}+\frac{b^2}{b+ca}+\frac{c^2}{c+ab}\ge\frac{a+b+c}{4}\)
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 ba so thuc duong thoa man dieu kien a+b+c=1
chung minh rang P=\(\sqrt{\frac{ab}{c+ab}}+\sqrt{\frac{bc}{a+bc}}+\sqrt{\frac{ca}{b+ca}}\le\frac{3}{2}\)
cho cac so a,b,c duong thoa man ab+bc+ca=1 chung minh : \(p=\frac{2a}{\sqrt{1+a^2}}+\frac{b}{\sqrt{1+b^2}}+\frac{c}{\sqrt{1+c^2}}\)
1. Cho a,b,c,d la cac so nguyen thoa man \(a^2=b^2+c^2+d^2\)
chung minh rang a.b.c.d + 2015 viet duoc duoi dang hieu cua 2 so chinh phuong.
2. Cho a,b la cac so duong thoa man dieu kien a+b=1. tim gia tri nho nhat cua bieu thuc
\(P=\frac{2+a}{\sqrt{2-a}}+\frac{2+b}{\sqrt{2-b}}\)
cho ca so a,b,c duong thoa man ab+bc+ca =1 chung minh \(P=\frac{2a}{\sqrt{1+a^2}}+\frac{b}{\sqrt{1+b^2}}+\frac{c}{\sqrt{1+c^2}}\le\frac{1}{4}\)
a,b,c la cac so thuc duong thoa man \(\frac{1}{1+a}+\frac{1}{1+b}+\frac{1}{1+c}=2\)
Max P=abc
6 tháng 3 2020 lúc 21:26
Cho a;b;c > 0 thỏa mãn a + b + c = 1
CMR: \(\frac{ab}{a^2+b^2}+\frac{bc}{b^2+c^2}+\frac{ca}{c^2+a^2}+\frac{1}{4}\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\ge\frac{15}{4}\)
cho a, b, c la cac so duong thoa man a\(a^2+b^2+c^2=3\) . Chung minh rang : \(\frac{1}{2-a}+\frac{1}{2-b}+\frac{1}{2-c}>=3\)