Cho 3 so x, y, z thoa man cac he thuc: \(\left(z-1\right)x-y=1\) va \(x+zy=2\)

Chmr: \(\left(2x-y\right)\left(z^2-z+1\right)=7\) va tim tat ca cac so nguyen x, y, z thoa man cac he thuc tren.

tim cac so nguyen duong x,y,z thoa man x^2+y^3+z^4

a)Tim tat ca cac so nguyen duong x, y , z thoa man: \(\frac{x+y\sqrt{2013}}{y+z\sqrt{2013}}\)la so huu ti, dong thoi x² + y²+ z² la so nguyen to.

b) Tim so tu nhien x, y thoa man: x(1+x+x²) = y(y-1).

cho x,y,z la cac so thuc duong thoa man x+y+z=1 tim  min A=x^3/(x^2+xy+y^2)+y^3/(y^2+yz+z^2)+z^3/(z^2+zx+x^2)

tim cac so nguyen x,y,z thoa man dieu kien sau

x^2=y-1

y^2=z-1

z^2=x-1

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

tim cac so nguyen to  x y z thoa man 3(x+y+z)=xyz

tim cac so nguyen x ,y,z thoa man /x-y/+/y-z/+/z-x/=2015

Tim cac so nguyen x, y, z thoa man x/y +y/z+z/x =y/x+/y+x/z=x+y+z=3