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Cho \(\hept{\begin{cases}a,b,c\ge0\\21ab+2bc+8ca\le12\end{cases}}\)
Tìm \(min\)\(E=\frac{1}{a}+\frac{2}{b}+\frac{3}{c}\)
\(abcd\le81\)Cho CMR : \(\hept{\begin{cases}a,b,c,d\ge0\\\frac{a}{a+1}+\frac{b}{b+1}+\frac{c}{c+1}+\frac{d}{d+1}\le\end{cases}}1\)
1, Cho \(\hept{\begin{cases}a,b>0\\a^2+b^2=1\end{cases}.}\)Tìm min A= \(\left(1+a\right)\left(1+\frac{1}{b}\right)+\left(1+b\right)\left(1+\frac{1}{a}\right)\)
2, Cho \(\hept{\begin{cases}a^2+2b^2\le3c^2\\a,b,c>0\end{cases}}\).Chứng minh : \(\frac{1}{a}+\frac{2}{b}\ge\frac{3}{c}\)
Cho \(\hept{\begin{cases}a,b,c\ge0\\\frac{a}{a+1}+\frac{b}{b+1}+\frac{c}{c+1}+\frac{d}{d+1}< 1\end{cases}}\)CMR \(abc\le\frac{1}{8}\)
moi nguoi oi giup em may cau nay voi1) Cho hept{begin{cases}a,b,c,dge0a+b+c+dle3end{cases}}tim max P2a+3b^2+4b^3+5b^42) Cho hept{begin{cases}a,b,cge0a+b+c3end{cases}}tim min Pleft(a-1right)^3+left(b-1right)^3+left(c-1right)^33) Cho hept{begin{cases}a,bge0;0le cle1a^2+b^2+c^23end{cases}} tim max,min Pab+bc+ca+3left(a+b+cright)4) Cho hept{begin{cases}a,b,cge0a+b+c3end{cases}}tim max Pasqrt{b}+bsqrt{c}+csqrt{a}-sqrt{abc}5) Cho hept{begin{cases}a,bge0;0le cle1a+b+c3end{cases}}tim max, min Pa^2+b^2+c...
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moi nguoi oi giup em may cau nay voi
1) Cho \(\hept{\begin{cases}a,b,c,d\ge0\\a+b+c+d\le3\end{cases}}\)tim max \(P=2a+3b^2+4b^3+5b^4\)
2) Cho \(\hept{\begin{cases}a,b,c\ge0\\a+b+c=3\end{cases}}\)tim min \(P=\left(a-1\right)^3+\left(b-1\right)^3+\left(c-1\right)^3\)
3) Cho \(\hept{\begin{cases}a,b\ge0;0\le c\le1\\a^2+b^2+c^2=3\end{cases}}\) tim max,min \(P=ab+bc+ca+3\left(a+b+c\right)\)
4) Cho \(\hept{\begin{cases}a,b,c\ge0\\a+b+c=3\end{cases}}\)tim max \(P=a\sqrt{b}+b\sqrt{c}+c\sqrt{a}-\sqrt{abc}\)
5) Cho \(\hept{\begin{cases}a,b\ge0;0\le c\le1\\a+b+c=3\end{cases}}\)tim max, min \(P=a^2+b^2+c^2+abc\)
em cam on nhieu
Cho \(\hept{\begin{cases}a+b=1\\a,b>0\end{cases}}\)
Tìm MIN A=\(a^2+b^2+\frac{1}{a^2}+\frac{1}{b^2}\)
Cho \(\hept{\begin{cases}a,b,c>0\\a+b+c=3\end{cases}}\)Tìm min \(A=3\left(a+b+c\right)+\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\)
Cho\(\hept{\begin{cases}a,b,c>0\\a+b+c=1\end{cases}}\) Tìm Min\(A=\frac{1}{a^2+b^2+c^2}+\frac{1}{abc}\)
\(Cho\hept{\begin{cases}a,b,c>0\\a+b+c=1\end{cases}}\)Tìm min \(P=\frac{a}{\sqrt{a+bc}}+\frac{b}{\sqrt{b+ca}}+\frac{c}{\sqrt{c+ba}}\)