Đáp án:
`a,`
Có : `x = 11`
`-> x + 1 = 12` `(1)`
Có :
`F (x) = x^{12} - 12x^{11} + 12x^{10} - 12x^9 +... + 12x^2 - 12x+1`
Thay `(1)` vào `F (x)` ta được :
`-> F (x) = x^{12} - (x+1)x^{11} + (x + 1)x^{10} - (x + 1)x^9 + ... + (x + 1)x^2 - (x + 1)x + 1`
`-> F (x) = x^{12} - x^{12} - x^{11} + x^{11} + x^{10} - x^{10} - x^9 + ... + x^3 + x^2 - x^2 - x + 1`
`-> F (x) = (x^{12} - x^{12}) + (-x^{11} + x^{11}) + ... + (x^2 - x^2) + (-x + 1)`
`-> F (x) = -x + 1`
`->F (11) = -11 + 1`
`->F (11) = -10`
Vậy `F (11) = -10`
$\\$
`b,`
`M = 2 118/119 × 1/117 - 1 116/117 × 1/119 - 3/117`
`-> M = 356/119 × 1/117 - 233/117 × 1/119 - 3/117`
`->M = 356 × 1/119 × 1/117 - 233 × 1/117 × 1/119 - 3 × 1/117`
`-> M = 1/117 × [356 × 1/119 - 233 × 1/119 - 3]`
`-> M = 1/117 × [(356 - 233) × 1/119 - 3]`
`-> M = 1/117 × [123 × 1/119 - 3]`
`-> M = 1/117 × [123/119 - 3]`
`->M = 1/117 × (-234)/119`
`-> M = (-2)/119`
Vậy `M = (-2)/119`
