Từ giả thiết: \(1\ge x+\dfrac{1}{y}\ge2\sqrt{\dfrac{x}{y}}\Rightarrow\dfrac{x}{y}\le\dfrac{1}{4}\Rightarrow\dfrac{y}{x}\ge4\)
\(\Rightarrow A=2\left(\dfrac{16x}{y}+\dfrac{y}{x}\right)+\dfrac{2020y}{x}\ge2.2\sqrt{\dfrac{16xy}{xy}}+2020.4=8096\)
\(A_{min}=8096\) khi \(\left(x;y\right)=\left(\dfrac{1}{2};2\right)\)
CHo \(x,y>0\) và xy=16 Tìm Min S\(=\dfrac{x^3}{16\left(y+16\right)}+\dfrac{y^3}{16\left(x+16\right)}+\dfrac{2021}{2022}\)
Cho 0<x,y,z<\(\dfrac{\sqrt{3}}{2}\) thỏa mãn xy+yz+zx=\(\dfrac{3}{4}\)
Tìm Min Q=\(\dfrac{4x^2}{x\left(32-4x^2\right)}+\dfrac{4y^2}{y\left(32-4y^2\right)}+\dfrac{4z^2}{z\left(32-4z^2\right)}\)
1. Cho a,b>0; a+b=1
Tìm min A=\(\left(a+\dfrac{1}{a}\right)^2+\left(b+\dfrac{1}{b}\right)^2+17\)
2. Cho x,y,x >0 t/m: \(x^2+y^2+z^2=3\)
CMR: \(\dfrac{xy}{z}+\dfrac{yz}{x}+\dfrac{zx}{y}\) ≥ 3
Cho x,y>1 thỏa mãn : \(x+y\le4\).Tìm min của biểu thức :
\(A=\dfrac{x^4}{\left(y-1\right)^2}+\dfrac{y^4}{\left(x-1\right)^4}\)
Tìm MIN:
\(G=\dfrac{1}{2}\left(\dfrac{x^{10}}{y^2}+\dfrac{y^{10}}{x^2}\right)+\dfrac{1}{4}\left(x^{16}+y^{16}\right)-\left(1+x^2y^2\right)^2\)
Cho \(a+\dfrac{1}{b}=b+\dfrac{1}{c}=c+\dfrac{1}{a}=x\)
\(Tính\) \(P=\dfrac{2022\left(x-y\right)\left(y-z\right)\left(z-x\right)}{2xy^2+2yz^2+2zx^2+3xyz}\)
chi x,y>1 tìm min p=\(\dfrac{\left(x^3+y^3\right)-\left(x^2+y^2\right)}{\left(x-1\right)\left(y-1\right)}\)
Cho x > 0, y > 0 thỏa mãn x + y ≤ 1. Tìm GTNN của M = \(\left(x+\dfrac{1}{x}\right)^2+\left(y+\dfrac{1}{y}\right)^2\).
Cho x,y>0 và x+y<=1,tìm GTNN: \(A=\left(\dfrac{1}{x}+\dfrac{1}{y}\right)\sqrt{1+x^2y^2}\)
