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\(\dfrac{3}{4}\times\dfrac{4}{5}\times\dfrac{5}{6}\times...\times\dfrac{x-1}{x}=\dfrac{1010}{1011}\)
\(\dfrac{3\times4\times5\times...\times\left(x-1\right)}{4\times5\times6\times...\times x}=\dfrac{1010}{1011}\)
\(\dfrac{3}{x}=\dfrac{1010}{1011}\)
\(x=\dfrac{3\times1011}{1010}=3\)
\(\dfrac{2^{4042}\cdot3^{2020}}{6^{2019}\cdot4^{1011}}=\dfrac{2^{4042}\cdot3^{2020}}{3^{2019}\cdot2^{2019}\cdot2^{2022}}\)
\(=3\cdot\dfrac{2^{2042}}{2^{4041}}=3\cdot2=6\)
a) 3m6cm = 306.cm
b) 1011 + 1011 + 1011 + 1011 = 1011 x4 = 4044 ….
c) Chữ số La Mã được viết XI đọc là:mười một
\(9,x-\sqrt{x}=\sqrt{x}\left(\sqrt{x}-1\right)\\ 10,a+3\sqrt{a}-10=\left(\sqrt{a}-1\right)\left(\sqrt{a}+5\right)\\ 11,x+\sqrt{x}-2=\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)\\ 12,x-5\sqrt{x}+6=\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)\)
9: \(x-\sqrt{x}=\sqrt{x}\left(\sqrt{x}-1\right)\)
10: \(a+3\sqrt{a}-10=\left(\sqrt{a}+5\right)\left(\sqrt{a}-2\right)\)
11: \(x+\sqrt{x}-2=\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)\)
12: \(x-5\sqrt{x}+6=\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)\)
Tìm x :
\(\left(\dfrac{2}{3}x-\dfrac{4}{9}\right).\left(\dfrac{1}{2}+\dfrac{3}{7}:x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(\dfrac{2}{3}x-\dfrac{4}{9}\right)=0\\\left(\dfrac{1}{2}+\dfrac{3}{7}:x\right)=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\dfrac{2}{3}x=\dfrac{4}{9}\\\dfrac{3}{7}:x=-\dfrac{1}{2}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=-\dfrac{6}{7}\end{matrix}\right.\)
Vậy.....
Tính :
\(\dfrac{1313}{1515}+\left(-\dfrac{1011}{5055}\right)=\dfrac{13}{15}-\dfrac{1}{5}=\dfrac{2}{3}\)
\(S=1010+1010^2+1010^3+...+1010^{1011}\)
Suy ra \(1010.S=1010^2+1010^3+1010^4+....+1010^{1012}\)
Nên\(1010.S-S=1010^{1012}-1010\)hay\(1009.S=1010^{1012}-1010\)
Khi đó \(S=\frac{1010^{1012}-1010}{1009}\)
S=1011+1010^2+1010^3+...+1010^1011
S=1+1010+1010^2+1010^3+...+1010^1011
1010.S=1010+1010^2+1010^3+1010^4+...+1010^1012
1010 S - S=1010^1012-1
1009 S=1010^1012-1
S=(1010^1012-1):1009
Đáp án D
⇔ log z - 1 log z = 1 1 - log x
⇔ 1 - log x = log z log z - 1
⇔ log x = - 1 log z - 1 ⇔ x = 10 1 1 - log z .
1011 x ( 3/4+5/4) = 1011 x 2 = 2022
\(1011\times\frac{3}{4}+1011\times\frac{5}{4}.\)
\(=1011\times\left(\frac{3}{4}+\frac{5}{4}\right)\)
\(=1011\times\frac{8}{4}\)
\(=1011\times2\)
\(=2022\)