Biết giới hạn lim x → 2 (x^10 + x^8 − 1280 )/(x^11 + x^7 − 2176 )= a /b , ( a , b > 0 , ( a , b ) = 1 ) . Giá trị của biểu thức P = a b bằng:

Có: $\underset{x\to 2}{\text{lim}}\frac{x^{10}+x^8-1280}{x^{11}+x^7-2176}=\underset{x\to 2}{\text{lim}}\frac{\left(x^{10}-2^{10}\right)+\left(x^8-2^8\right)}{\left(x^{11}-2^{11}\right)+\left(x^7-2^7\right)}$

\[ = \mathop {\lim }\limits_{x \to 2} \frac{{(x - 2)\left( {{x^9} + 2{x^8} +  \ldots  + {2^8}x + {2^9}} \right) + (x - 2)\left( {{x^7} + 2{x^6} +  \ldots  + {2^6}x + {2^7}} \right)}}{{(x - 2)\left( {{x^{10}} + 2{x^9} +  \ldots  + {2^9}x + {2^{10}}} \right) + (x - 2)\left( {{x^6} + 2{x^5} +  \ldots  + {2^5}x + {2^6}} \right)}}\]

 $=\underset{x\to 2}{\text{lim}}\frac{\left(x^9+2x^8+\dots +2^{8}x+2^9\right)+\left(x^7+2x^6+\dots +2^{6}x+2^7\right)}{\left(x^{10}+2x^9+\dots +2^{9}x+2^{10}\right)+\left(x^6+2x^5+\dots +2^{5}x+2^6\right)}$

\( = \frac{{10 \cdot {2^9} + 8 \cdot {2^7}}}{{11 \cdot {2^{10}} + 7 \cdot {2^6}}} = \frac{{32}}{{61}}\).

Khi đó, \(P = ab = 32 \cdot 61 = 1952\). Chọn C.