`#Mon`
`@\text{ Bài 9:}`
`\frac{a}{b}+\frac{b}{c}+\frac{c}{a}-(\frac{b}{a}+\frac{c}{b}+\frac{a}{c})=0`
`<=>\frac{a-c}{b}+\frac{b-a}{c}+\frac{c-b}{a}=0`
`<=>\frac{a-c}{b}+\frac{c-a+b-c}{c}+\frac{c-b}{a}=0`
`<=>(a-c)(\frac{1}{b}-\frac{1}{c})+(b-c)(\frac{1}{c}-\frac{1}{a})=0`
`<=>\frac{(a-c)(c-b)(b-a)}{abc}=0`
`<=>a=b; b=c; c=a`
`Nếu` `a=b=>\frac{a}{c}+\frac{c}{a}+1=2a+c=3(**)`
`Thay` `vào` `(**)`
`=>a=c=1=>a=b=c=1`
`Tương` `tự` `nếu` `a=b` `hoặc` `c=a`
`\text{ Đều ra a=b=c=1}`
`Vậy` `( a;b;c)=(1;1;1)` `là` `nghiệm`
`@\text{ Bài 10:}`
`Giả` `sử:` `0<x<=y<=z`
`=>x+y+z<=z+z+z=3z`
`=>xyz<=3z`
`=>xy<=3`
`=>xy in {1;2;3}`
`+)xy=1=>x=1;y=1=>z+2=z(\text{ vô lí})`
`+)xy=2;x<=y=>x=1;y=2=>z +3=2z<=>z=3( t/m x<=y<=z)`
X`xy=3;x<=y=>x=1;y=3=>z+4=3z<=>z=2(loại)`
`=>(x;y;z)=(1;2;3);(1;3;2);(2;1;3);(2;3;1);(3;1;2);(3;2;1)`
