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\(\frac{5^4.20^4}{25^5.4^5}=\frac{5^4.4^4.5^4}{5^{10}.4^5}=\frac{5^8.4^4}{5^8.5^2.4^4.4}=\frac{1}{25.4}=\frac{1}{100}\)
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a) \(A=\frac{5^4.20^4}{25^5.4^5}=\frac{5^4.\left(2^2.5\right)^4}{5^{2^5}.\left(2^2\right)^5}=\frac{5^8.2^8}{5^{10}.2^{10}}=\frac{1}{\left(5^{10}:5^8\right).\left(2^{10}:2^8\right)}=\frac{1}{5^2.2^2}=\frac{1}{25.4}=\frac{1}{100}\)
b) \(B=\frac{2^{30}.5^7+2^{13}.5^{27}}{2^{27}.5^7+2^{10}.5^{27}}\)\(=\frac{2^3+2^3}{1}=\frac{8+8}{1}=16\)
c) \(C=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...........+\frac{1}{2^{100}}\)
\(\Rightarrow2C=1+\frac{1}{2}+\frac{1}{2^2}+..........+\frac{1}{2^{99}}\)
\(\Rightarrow2C-C=\left(1+\frac{1}{2}+\frac{1}{2^2}+.........+\frac{1}{2^{99}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...........+\frac{1}{2^{100}}\right)\)
\(\Rightarrow C=1-\frac{1}{2^{100}}\)
d) \(D=1+\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+.........+\frac{1}{5^{100}}\)
\(\Rightarrow5D=5+1+\frac{1}{5^2}+\frac{1}{5^3}+...........+\frac{1}{5^{101}}\)
\(\Rightarrow5D-D=\left(5+1+\frac{1}{5^2}+\frac{1}{5^3}+.........+\frac{1}{5^{101}}\right)-\left(1+\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+..........+\frac{1}{5^{100}}\right)\)
\(\Rightarrow4D=5-\frac{1}{5^{101}}\)
\(\Rightarrow D=\frac{5-\frac{1}{5^{101}}}{4}\)
a) \(A=\frac{5^4x20^4}{25^5x4^5}=\frac{5^4x\left(2^2x5\right)^4}{\left(5^2\right)^5x\left(2^2\right)^5}=\frac{5^8.2^8}{5^{10}.2^{10}}=\frac{1}{5^2x2^2}=\frac{1}{25.4}=\frac{1}{100}\)
b) \(B=\frac{2^{30}x5^7+2^{13}x5^{27}}{2^{27}x5^7+2^{10}x5^{27}}=\frac{2^{13}.5^7.\left(2^{17}+5^{20}\right)}{2^{10}.5^7.\left(2^{17}+5^{20}\right)}=2^3=8\)
c) \(C=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{100}}\)
\(\Rightarrow2C=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{99}}\)
\(\Rightarrow2C-C=1-\frac{1}{2^{100}}\)
\(C=1-\frac{1}{2^{100}}\)
phần d bn lm tương tự như phần c nha!
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Thu gọn Q(x) = 5x4 - x5 - x2 - 2x3 + 3x2 + 3x - 2x4 + 5
= -x5 + 3x4 - 2x3 + 2x2 + 3x + 5
Hệ số của x4là 3. Chọn B
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+) Ta có
2 g ( x ) = 2 − x 4 + 2 x 3 − 3 x 2 + 4 x + 5 = − 2 x 4 + 4 x 3 − 6 x 2 + 8 x + 10 Ta có f ( x ) − 2 ⋅ g ( x ) = 5 x 4 + 4 x 3 − 3 x 2 + 2 x − 1 − − 2 x 4 + 4 x 3 − 6 x 2 + 8 x + 10 = 5 x 4 + 4 x 3 − 3 x 2 + 2 x − 1 + 2 x 4 − 4 x 3 + 6 x 2 − 8 x − 10 = 5 x 4 + 2 x 4 + 4 x 3 − 4 x 3 + − 3 x 2 + 6 x 2 + ( 2 x − 8 x ) − 1 − 1 = 7 x 4 + 3 x 2 − 6 x − 11
Hệ số cần tìm là -11
Chọn đáp án C
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Ta có p(x) + q(x)
Bậc của đa thức p ( x ) + q ( x ) = 4 x 4 + 6 x 3 - 6 x 2 + 6 x - 6 l à 4
Chọn đáp án C
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(x-1)^2+|2y-3|=0
=>x-1=0 và 2y-3=0
=>x=1 và y=1,5
B=4*1^20+5*1^2*1,5-6*1,5+2
=4+7,5-9+2
=4,5