\[\begin{array}{l}
Giai:\\
Ta\,\,co:\,\,xy + yz + zt + tx = xyzt\\
= y(x + z) + t(x + z) = xyzt\\
= (x + z)(y + t) = xyzt\,\,\,(*)\\
= > y(x + z) \vdots t\,\,\,\,\,\,\,\, = > \,xay\,\,ra\,\,2\,\,th:\\
TH1:y \vdots t\\
= > y = t\\
Tu\,\,(*) = > 2y(x + z) = xz{y^2}\\
= > 2(x + z) = xzy\\
neu\,\,x = 2 = > 2(2 + z) = 2zy\\
= > 2 + z = zy\\
= > 2 = zy - z\\
= > 2 = z(y - 1)\\
= > z = 2;y = 2\\
Tu\,\,(*) = > (2 + 2)(2 + t) = 2.2.2t\\
= > 4(2 + t) = 8t\\
= > 2 + t = 2t\\
= > t = 2\\
neu\,\,z = 2 = > 2(2 + x) = 2xy\\
= > 2 + x = xy\\
= > 2 = xy - x\\
= > 2 = x(y - 1)\\
= > x = 2;y = 2\\
Tu\,\,(*) = > (2 + 2)(2 + t) = 2.2.2t\\
= > 4(2 + t) = 8t\\
= > 2 + t = 2t\\
= > t = 2\\
neu\,\,y = 2 = > 2(x + z) = 2xz\\
= > x + z = xz\\
= > x = xz - z\\
= > x = z(x - 1)\\
= > x - 1 = 1;\,\,z = x\\
= > x = 2;\,\,z = 2\\
Tu\,\,(*) = > (2 + 2)(2 + t) = 2.2.2t\\
= > 4(2 + t) = 8t\\
= > 2 + t = 2t\\
= > t = 2\\
TH2
x + z) \vdots t\\
Xet\,\,cac\,\,th:\\
x > 2;z > 2\\
x = 2\,\,hoac\,\,z = 2\\
x = z = 2\\
Ta\,\,van\,\,thu\,\,duoc\,\,ket\,\,qua\,\,x = y = z = t = 2\\
Bai\,\,nay\,\,hoi\,\,dai,\,mong\,\,cac\,\,ban\,thong\,\,cam!\,Ai\,\,rut\,\,gon\,\,duoc\,\,thi\,\,giup\,\,{\mathop{\rm minh}\nolimits} \,\,nha!
\end{array}\]
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