Các câu hỏi tương tự
cho \(\frac{x}{y}=\frac{y}{z}=\frac{z}{t}\)cm \(\left(\frac{x+y+z}{y+z+t}\right)^3\) =\(\frac{x}{t}\)
cho ba số khác nhau là x,y,z. CMR:
\(\frac{y-z}{\left(x-y\right)\left(x-z\right)}+\frac{z-x}{\left(y-z\right)\left(y-x\right)}+\frac{x-y}{\left(z-x\right)\left(z-y\right)}=\frac{x}{x-y}+\frac{z}{y-z}+\frac{y}{z-x}\)
cho các số dương x,y,z,t . Chứng minh: \(\frac{40}{3}\le\frac{x}{y+z+t}+\frac{y}{z+t+x}+\frac{z}{t+x+y}+\frac{t}{x+y+z}+\frac{y+z+t}{x}+\frac{z+t+x}{y}+\frac{t+x+y}{z}+\frac{x+y+z}{t}\)
tìm nghiệm nguyên
\(\frac{1}{x^2\left(x^2+y^2\right)}+\frac{1}{\left(x^2+y^2\right)\left(x^2+y^2+z^2\right)}+\frac{1}{x^2\left(x^2+y^2+z^2\right)}\) = 1
Tìm nghiệm nguyên dương:
\(\frac{x}{y}+\frac{y}{z}+\frac{z}{t}+\frac{t}{x}=3\)
Cho x,y,z ko âm t/m xyz=1. CMR
\(\frac{1}{\left(x+1\right)^2+y^2+1}+\frac{1}{\left(y+1\right)^2+z^2+1}+\frac{1}{\left(z+1\right)^2+x^2+1}\le\frac{1}{2}\)
Giải giúp mình với
CMR \(\frac{y-z}{\left(x-y\right).\left(x-z\right)}+\frac{z-x}{\left(y-z\right).\left(y-x\right)}+\frac{x-y}{\left(z-x\right).\left(z-y\right)}=\frac{2}{x-y}+\frac{2}{y-z}+\frac{2}{z-x}\)Cho a,b,c,x,y,z \(\ne\)0 và \(a+b+c=x+y+z=\frac{x}{a}+\frac{y}{b}+\frac{z}{c}\)CMR \(a^2x+b^2y+c^2z=0\)Thanks nhiều ạ
Cho x,y,z > 0 CMR
\(\frac{\left(y+z\right)^2}{x}+\frac{\left(x+z\right)^2}{y}+\frac{\left(x+y\right)^2}{z}\ge4\left(x+y+z\right)\)
Cho x,y,z>0. Cmr \(\frac{x^3}{\left(y+2z\right)^2}+\frac{y^3}{\left(z+2x\right)^2}+\frac{z^3}{\left(x+2y\right)^2}\ge\frac{2\left(x+y+z\right)}{9}\)
biết x khác 0 , y khác 0 , z khác 0 và x+y+z=0
CMR : \(\left(\frac{x-y}{z}+\frac{y-z}{x}-\frac{z-x}{y}\right)\)\(\left(\frac{z}{x-y}-\frac{x}{y-z}+\frac{y}{z-x}\right)\)= 9