Các câu hỏi tương tự
Cho x,y,z nguyen duong thoa man x+y-z+1=0
Tim GTLN cua \(P=\frac{x^3y^3}{\left(x+yz\right)\left(y+xz\right)\left(z+xy\right)^2}\)
1 cho 3 so thuc duong thoa man x^2010+y^2010+z^20103 tim gia tri lon nhat cua x^2+y^2+z^22 cho a;b;c duong c/m frac{1}{a}+frac{1}{b}+frac{1}{c}hoac3left(frac{1}{a+2b}+frac{1}{b+2c}+frac{1}{c+2a}right)3 tim gia tri nho nhat cua sqrt{a^2+ab+b^2}+sqrt{b^2+bc+c^2}+sqrt{c^2+ac+a^2} voi a+b+c14 cho a;b;c;d va A;B;C;D la cac so duong thoa man frac{a}{A}frac{b}{B}frac{c}{C}frac{d}{D}C/ M sqrt{aA}+sqrt{bB}+sqrt{cC}+sqrt{dD}sqrt{left(a+b+c+dright)left(A+B+C+Dright)}5 tim gia tr...
Đọc tiếp
1 cho 3 so thuc duong thoa man x^2010+y^2010+z^2010=3 tim gia tri lon nhat cua x^2+y^2+z^2
2 cho a;b;c duong c/m \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}>hoac=3\left(\frac{1}{a+2b}+\frac{1}{b+2c}+\frac{1}{c+2a}\right)\)
3 tim gia tri nho nhat cua \(\sqrt{a^2+ab+b^2}+\sqrt{b^2+bc+c^2}+\sqrt{c^2+ac+a^2}\) voi a+b+c=1
4 cho a;b;c;d va A;B;C;D la cac so duong thoa man \(\frac{a}{A}=\frac{b}{B}=\frac{c}{C}=\frac{d}{D}\)C/ M \(\sqrt{aA}+\sqrt{bB}+\sqrt{cC}+\sqrt{dD}=\sqrt{\left(a+b+c+d\right)\left(A+B+C+D\right)}\)
5 tim gia tri lon nhat cua \(\frac{yz\sqrt{x-1}+xz\sqrt{y-2}+xy\sqrt{z-3}}{xyz}\)
6 phan tich da thuc thanh nhan tu \(y-5x\sqrt{y}+6x^2\)
7 cho x;y;z>0 xy+yz+xz=1 tinh \(x\sqrt{\frac{\left(1+y^2\right)\left(1+z^2\right)}{1+x^2}}+y\sqrt{\frac{\left(1+x^2\right)\left(1+z^2\right)}{1+y^2}}+z\sqrt{\frac{\left(1+x^2\right)\left(1+y^2\right)}{1+z^2}}\)
8 cho a;b;c >0 c/m \(\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}
1. Tim x,y,z biet: \(\frac{1}{2}\left(x+y+z\right)-3=\sqrt{x-2}+\sqrt{y-3}+\sqrt{z-4}\)
2. Chox,y,z > 0 thoa man \(x+y+z+\sqrt{xyz}=4\) . Tinh \(A=\sqrt{x\left(4-y\right)\left(4-z\right)+\sqrt{y\left(4-z\right)\left(4-x\right)}+\sqrt{z\left(4-x\right)\left(4-y\right)}-\sqrt{xyz}}\)
Cho x,y,z dương thỏa mãn xyz=1.CMR :
1) A\(=\frac{1}{x^2+x+1}+\frac{1}{y^2+y+1}+\frac{1}{z^2+z+1}\ge1\)
2) B\(=\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(y+1\right)\left(y+2\right)}+\frac{1}{\left(z+1\right)\left(z+2\right)}\ge\frac{1}{2}\)
Cho x,y,z>0 va xyz=1. Tim Min cua \(P=\frac{x^2\left(y+z\right)}{y\sqrt{y}+2z\sqrt{z}}+\frac{y^2\left(z+x\right)}{z\sqrt{z}+2x\sqrt{x}}+\frac{z^2\left(x+y\right)}{x\sqrt{x}+2y\sqrt{y}}\)
Cho x y z > 0 và xyz=1.Tìm \(P=\frac{x^3}{\left(1+x^2\right)\left(1+y^2\right)}a+\frac{y^3}{\left(1+y^2\right)\left(1+z^2\right)}+\frac{z^3}{\left(1+z^2\right)\left(1+x^2\right)}\)
Cho các số thực x, y, z thõa mãn xyz = 1. Chứng minh rằng:
\(\frac{1}{\left(2+x\right)\left(2+\frac{1}{y}\right)}+\frac{1}{\left(2+y\right)\left(2+\frac{1}{z}\right)}+\frac{1}{\left(2+z\right)\left(2+\frac{1}{x}\right)}\le\frac{1}{3}\)
x;y;z>0. CMR: \(\left(1+\frac{x}{y}\right)\left(1+\frac{y}{z}\right)\left(1+\frac{z}{x}\right)\ge2+\frac{2\left(x+y+z\right)}{\sqrt[3]{xyz}}\)
Giả sử x,y,z là 3 số thực dương thỏa mãn điều kiện x+y+z=xyz. Chứng minh rằng:
\(\frac{x}{1+x^2}+\frac{2y}{1+y^2}+\frac{3z}{1+z^2}=\frac{xyz\left(5x+4y+3z\right)}{\left(x+y\right)\left(y+z\right)\left(z+x\right)}\)