`#Mon`
`P=\frac{a+b+c-2}{(a^2-a+1)(b^2-b+1)(c^2-c+1)}`
`=\frac{a+b+c-2}{(a^2-2.\frac{1}{2}.a+\frac{1}{4}+\frac{3}{4})(b^2-2.b.\frac{1}{2}+\frac{1}{4}+\frac{3}{4})(c^2-2.\frac{1}{2}.c+\frac{1}{4}+\frac{3}{4})}`
`=\frac{a+b+c-2}{[(a-\frac{1}{2})^2+\frac{3}{4}][(b-\frac{1}{2})^2+\frac{3}{4}][(c-\frac{1}{2})^2+\frac{3}{4}]}`
`@(a-\frac{1}{2})^2+\frac{3}{4}>=\frac{3}{4}`
`@(b-\frac{1}{2})^2+\frac{3}{4}>=\frac{3}{4}`
`@(c-\frac{1}{2})^2+\frac{3}{4}>=\frac{3}{4}`
`P_{MAX}` `\text{ khi dấu "=" xảy ra và}` `a=b=c=\frac{1}{2}`
`P=\frac{\frac{1}{2}.3-2}{(\frac{3}{4})^3}`
`=\frac{\frac{3}{2}-2}{(\frac{3}{4})^3}`
`=\frac{-\frac{1}{4}}{(\frac{3}{4})^3}`
`=-\frac{1}{4}.\frac{4^3}{9^3}`
`=-\frac{4^2}{9^3}`
