tìm số hữu tỉ x,y,z biết:
a. \(\left(x-\frac{1}{3}\right)\left(y-\frac{1}{2}\right)\left(z-5\right)=0\)và \(x+2=y+1=z+3\)
b. \(x+y=xy=x:y\)( y khác 0 )
c. \(x-y=xy=x:y\) ( y khác 0 )
d. \(x\left(x+y+z\right)=-5\) ; \(y\left(x+y+z\right)=9\) ; \(z\left(x+y+z\right)=5\)
b)xy=x:y=>y2=1
=>y=1 hoặc y=-1
*)y=1
=>x+1=x
=>0x=-1(L)
*)y=-1
=>x-1=-x
=>2x=1
=>x=1/2
Vậy y=-1 x=1/2
c)xy=x:y=>y2=1
=>y=1 hoặc y=-1
*)y=1
=>x-1=x
=>0x=1(L)
*)y=-1
=>x+1=-x
=>2x=-1
=>x=-1/2
Vậy y=-1 x=-1/2
d)x(x+y+z)+y(x+y+z)+z(x+y+z)=-5+9+5=9
=>(x+y+z)2=9
=>x+y+z=3 hoặc x+y+z=-3
*)x+y+z=3
=>x=-5:3=-5/3
y=9:3=3
z=5:3=5/3
*)x+y+z=-3
=>x=-5:(-3)=5/3
y=9:(-3)=-3
z=5:(-3)=-5/3