Các câu hỏi tương tự
cho cac so thuc thoa man a+b+c=6 va 0 =<a,b,c=<4
Tim Max P=a2+b2+c2+ab+ac+bc
CHO a,b,c>0; a+b+c =\(\frac{2}{a+b}+\frac{2}{b+c}+\frac{2}{c+a}\)
TÌM MAX: Q = ab+bc+ca
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:
\(Q=\frac{1}{\sqrt{a^2+1}}+\frac{1}{\sqrt{b^2+1}}+\frac{1}{\sqrt{c^2+1}}\)
Cho a, b, c > 0 và \(\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}=\dfrac{1}{3}\) .
Tìm MAX : A= \(\dfrac{1}{a^2+bc}+\dfrac{1}{b^2+ca}+\dfrac{1}{c^2+ab}\)
cho a,b,c>0: ab+bc+ca=1.tìm Max F\(\frac{1}{a^2+2}+\frac{1}{b^2+2}+\frac{1}{c^2+2}\)
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 thỏa mãn 1/a+1/b+1/c=3. Tìm Max P=\(\frac{1}{\sqrt{a^2-ab+b^2}}+\frac{1}{\sqrt{b^2-bc+c^2}}+\frac{1}{\sqrt{c^2-ca+a^2}}\)
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 . Chứng minh rằng :
\(\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\ge\frac{3}{2}+\frac{7}{16}\cdot\frac{max\left\{\left(a-b\right)^2,\left(b-c\right)^2,\left(c-a\right)^2\right\}}{ab+bc+ca}\)