\(P=\left(a+\frac{1}{4a}\right)+\left(b+\frac{1}{4b}\right)+\frac{3}{4a}+\frac{35}{4b}\ge2\sqrt{a.\frac{1}{4a}}+2.\sqrt{b.\frac{1}{4b}}+\frac{3}{4.\frac{1}{2}}+\frac{35}{4.\frac{1}{2}}\)
\(P\ge\frac{2.1}{2}+\frac{2.1}{2}+\frac{3}{4.\frac{1}{2}}+\frac{35}{4.\frac{1}{2}}=21\)
P min =21 khi a=b =1/2
cho a,b>0 thỏa mãn a+b=1. tim MIN Q=\(a+b+\frac{1}{a}+\frac{1}{b}\)
cho a,b là các số dương tm a+b<1
tim min \(S=\frac{a^2}{1-a}+\frac{b^2}{1-b}+a+b+\frac{1}{a+b}\)
Bài: Cho a, b >0, (a+1)(b+1)=\(\frac{9}{4}\) Chứng minh : M min =?, a=?,b=?
Cho \(\hept{\begin{cases}ab+bc+ca=3\\a,b,c>0\end{cases}}\)
Tim Min P= \(\frac{a}{1+2b^3}+\frac{b}{1+2c^3}+\frac{c}{1+2a^3}\)
Cho a+b=5, a >0, b>0
Tìm min P = \(\frac{1}{a}+\frac{1}{b}\)
cho a,b>0; a+b-1>0 :\(\left(a+b-1\right)^2=ab\)
tìm min của \(\frac{1}{ab}+\frac{1}{a^2+b^2}+\frac{\sqrt{ab}}{a+b}\)
cho a,b>0 và \(\frac{1}{a}+\frac{1}{b}\le\frac{1}{2}\)
Tìm min \(\sqrt{a}+\sqrt{b}-\frac{1}{a+b}\)
Cho a,b,c>0 thỏa mãn a+b+c=1
Tìm Min: A=\(\frac{a}{a^2+1}+\frac{b}{b^2+1}+\frac{c}{c^2+1}+\frac{1}{9abc}\)
cho a,b,c > 0 va abc = 0 tim min
\(a^3+b^3+c^3+\frac{2c}{a+b}+\frac{2a}{b+c}+\frac{2b}{c+a}\)
