Giả sử \(1\le x\le y\le z\) Khi đó
phương trình đã cho \(\Leftrightarrow xyz=x+y+z\le3z\Rightarrow x.y\le3\) Vì x,y,z thuộc Z+ \(\Rightarrow x.y\in\left\{1;2;3\right\}\)
Nếu \(xy=1\Rightarrow x=y=1\Rightarrow2+z=z\left(S\right)\)
Nếu \(xy=2\Rightarrow x=1;y=2;z=3\)
Nếu \(x.y=3\Rightarrow x=1;y=3\Rightarrow z=2\) <y (vô lí)
Vậy x;y;z là hoán vị của 1;2;3
cho x,y,z la cac so huu ti duong thoa man x+1/yz y +1/xz z+1/xy la cac so nguyen tim gia tri lon nhat cua bieu thuc A=x+y^2+z^3
c1: Tap hop cac gia tri nguyen cua x thoa man \(\left(x+\frac{5}{4}\right)\left(x-\frac{19}{7}\right)\)<0
c2: Neu x,y la cac so nguyen thoa man 2xy+4y=6 thi y co the nhan nhung gia tri nam trong tap hop nao
c3: tim 3 so x,y,z biet x+y=8,x+z=10,y+z=12
C4: Gia tri cua x thoa man (x+3)^2=25 va x^3>0 la x=
Tim cac so nguyen duong x;y;z thoa man x!+y!=10.z+9
tim cac so nguyen x , y , z thoa man :
/x-y/+/y-z/+/x-z/=2015
nham la tri tuyet doi
tim cac so x y z nguyen duong thoa man x3+3x2+5=5y va x+3=5z
tim cac so x,y,z ko am thoa man x+6y=12 va 4x +5z=2018 sao cho F=x+y+z co gia tri lon nhat
tim cac so nguyen x ,y,z thoa man /x-y/+/y-z/+/z-x/=2015
bai 1:Tim x,y,z \(\varepsilon\)Z ,sao cho :|x-y|+|y-z|+|z-x|+|z-t|+|t-x|=2003
bai 2:Cho bieu thuc:E=\(\frac{5-x}{x-2}\)tim gia tri nguyen cua x de
a) E co gia tri nguyen
b)E co gia tri nho nhat
tim cac so nguyen to x y z thoa man 3(x+y+z)=xyz
