Thực hiện phép tính: x - 4 16 - x 2 2 x + 8 + 1 x - 1 .
A. - x 2 + 5 x + 7 ( 4 - x ) ( x - 1 )
B. x 2 + 5 x + 7 ( 4 - x ) ( x - 1 )
C. - 2 x 2 - 6 x + 7 ( 4 + x ) ( x - 1 )
D. 2 x 2 - 6 x - 7 ( 4 + x ) ( x - 1 )
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\(=\dfrac{1+x+1-x}{1-x^2}+\dfrac{2}{1+x^2}+...+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{2}{1-x^2}+\dfrac{2}{1+x^2}+...+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{2+2x^2+2-2x^2}{1-x^4}+...+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{4}{1-x^4}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+...+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{4+4x^4+4-4x^4}{1-x^8}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{8+8x^8+8-8x^8}{1-x^{16}}+\dfrac{16}{1+x^{16}}\)
\(=\dfrac{16+16x^{16}+16-16x^{16}}{1-x^{32}}=\dfrac{32}{1-x^{32}}\)
\(\dfrac{1}{1-x}\)+\(\dfrac{1}{1+x}\)+\(\dfrac{2}{1+x^2}\)+\(\dfrac{4}{1+x^4}\)+\(\dfrac{8}{1+x^8}\)+\(\dfrac{16}{1+x^{16}}\)
=
=\(\dfrac{4}{1-x^4}\)+\(\dfrac{4}{1+x^4}\)+\(\dfrac{8}{1+x^8}\)+\(\dfrac{16}{1+x^{16}}\)
=\(\dfrac{8}{1-x^8}\)+\(\dfrac{8}{1+x^8}\)+\(\dfrac{16}{1+x^{16}}\)
=\(\dfrac{16}{1-x^{16}}\)+\(\dfrac{16}{1+x^{16}}\)
=\(\dfrac{32}{1-x^{32}}\)
\(A=\dfrac{1}{1-x}+\dfrac{1}{1+x}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(A=\left(\dfrac{1+x}{\left(1-x\right)\left(1+x\right)}+\dfrac{1-x}{\left(1+x\right)\left(1-x\right)}\right)+...+\dfrac{16}{1+x^{16}}\)
\(A=\dfrac{1+x+1-x}{1-x^2}+\dfrac{2}{1+x^2}+...+\dfrac{16}{1+x^{16}}\)
\(A=\dfrac{2}{1-x^2}+\dfrac{2}{1+x^2}+...+\dfrac{16}{1+x^{16}}\)
Tiếp tục các bước như ở dòng 2 và 3 ta có :
\(A=\dfrac{16}{1-x^{16}}+\dfrac{16}{1+x^{16}}\)
\(A=\dfrac{16\left(1+x^{16}\right)}{\left(1-x^{16}\right)\left(1+x^{16}\right)}+\dfrac{16\left(1-x^{16}\right)}{\left(1+x^{16}\right)\left(1-x^{16}\right)}\)
\(A=\dfrac{16+16x^{16}+16-16x^{16}}{1-x^{32}}\)
\(A=\dfrac{32}{1-x^{32}}\)
\(25\cdot\left\{8\cdot\left[12-4+8\left(16\div80\right)\right]\right\}\)
\(=25\cdot\left\{8\cdot\left[12-4+8\cdot0,2\right]\right\}\)
\(=25\cdot\left\{8\cdot8+1,6\right\}\)
\(=25\cdot\left(64+1,6\right)\)
\(=25\cdot65,6=1640\)
b)\(2016\cdot0+1\left(207+\frac{0}{4579}\right)=0+1\cdot207=207\)
c)\(15\cdot\left\{2100\div\left[251-\left(16+84\cdot2\right)\right]\right\}\)
\(=15\cdot\left\{2100\div\left[251-\left(16+168\right)\right]\right\}\)
\(=15\cdot\left\{2100\div\left[251-184\right]\right\}\)
\(=15\cdot\left(2100\div67\right)\)
\(=15\cdot\frac{2100}{67}=\frac{31500}{67}\)
Chọn đáp án C