cho a,b,c>=0 va (a+b)(b+c)(a+c)>0. Tim TNN cua
\(\frac{a\left(b+c\right)}{b^2+bc+c^2}+\frac{b\left(a+c\right)}{a^2+ac+c^2}+\frac{c\left(a+b\right)}{a^2+ab+b^2}\)
cho a,b,c>=0 tm a+b+c=1009. tim max
P=\(\sqrt{2018a+\frac{\left(b-c\right)^2}{2}}+\sqrt{2018b+\frac{\left(c-a\right)^2}{2}}+\sqrt{2018c+\frac{\left(a-b\right)^2}{2}}\)
Cho ab+bc+ca+abc=4 với a,b,c>0. C/m \(\frac{1}{a+2}+\frac{1}{b+2}+\frac{1}{c+2}=1\).
b) Tìm max \(P=\frac{1}{\sqrt{2\left(a^2+b^2\right)+4}}+\frac{1}{\sqrt{2\left(c^2+b^2\right)+4}}+\frac{1}{\sqrt{2\left(c^2+a^2\right)+4}}\)
Cho \(a,b,c>0\) thỏa mãn \(3\left(a^2+b^2+c^2\right)+ab+bc+ca=12\) Tìm Max:
\(P=\frac{a^2+b^2+c^2}{a+b+c}+ab+bc+ca\)
Cho \(a,b,c>0\) thỏa mãn \(abc=a+b+c+2\) Tìm Max:
\(Q=\frac{1}{\sqrt{a^2+1}}+\frac{1}{\sqrt{b^2+1}}+\frac{1}{\sqrt{c^2+1}}\)
câu 1 :Cmr a)\(\frac{a^2+b^2}{2}\ge\left(\frac{a+b}{2}\right)^2\)
b) \(\frac{a^3+b^3+c^3}{3}\ge\left(\frac{a+b+c}{3}\right)^3\)
câu 2 : cho a+b=1 .Cm \(\frac{1}{a+1}+\frac{1}{b+1}\ge\frac{4}{3}\)
câu 3: cho a+b+c=1và a,b,c>0.CMR \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\ge9\)
câu 4 Tim max của : ab+2(a+b) ...biết a2+b2=1
Cho a,b,c > 0 thỏa mãn a + b + c = abc . Tìm
\(A_{max}=\frac{a}{\sqrt{bc\left(1+a^2\right)}}+\frac{b}{\sqrt{ca\left(1+b^2\right)}}+\frac{c}{\sqrt{ab\left(1+c^2\right)}}\)
cho a,b,c khac 0 va a+b+c=0 . tinh Q=\(\frac{1}{a^2+b^2-c^2}+\frac{1}{b^2+c^2-a^2}+\frac{1}{a^2+c^2-b^2}\)
cho a,b,c >0 va abc=1 c/m
\(\frac{1+ab^2}{c^3}+\frac{1+bc^2}{a^3}+\frac{1+ca^2}{b^3}>=\frac{18}{a^3+b^3+c^3}\)
1. Cho a,b,c>0 và a^2000+b^2000+c^2000=3. Tìm max P=a^2+b^2+c^2
2. Cho a,b,c là 3 cạnh tam giác. Tìm max \(A=\left(3-\frac{b+c}{a}\right)\left(3-\frac{c+a}{b}\right)\left(3-\frac{a+b}{c}\right)\)
