9 x (12+X)=120
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BD
1
6 tháng 8 2017
\(\dfrac{10.4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\dfrac{5.2.2^{12}.3^{10}+3^9.2^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\dfrac{5.2^{13}.3^{10}+2^{12}.3^{10}.5}{2^{11}.3^{11}\left(2.3-1\right)}=\dfrac{2^{12}.3^{10}.5\left(2+1\right)}{2^{11}.3^{11}.5}\)
\(=\dfrac{2^{11}.2.3^{10}.5.3}{2^{11}.3^{10}.3.5}=2\)
YN
19 tháng 9 2021
\(\frac{15}{x-9}=\frac{20}{y-12}=\frac{40}{z-24}\) và \(x.y=1200\) (Sửa đề)
Ta có:
\(\frac{x-9}{15}=\frac{y-12}{20}=\frac{z-24}{40}\Rightarrow\frac{x}{15}.\frac{9}{15}=\frac{y}{20}.\frac{12}{20}=\frac{z}{40}.\frac{24}{40}\)
Mà \(\frac{9}{15}=\frac{12}{20}=\frac{24}{40}=\frac{3}{5}\Rightarrow\frac{x}{15}=\frac{y}{20}=\frac{z}{40}\)
\(\Rightarrow\frac{x^2}{15^2}=\frac{y^2}{20^2}=\frac{z^2}{40^2}=\frac{x.y}{15.20}=\frac{1200}{300}=2^2\)
\(\Rightarrow x^2=2^2.15=\left(2.15\right)^2=30^2\Rightarrow x=\pm30\)
\(\Rightarrow y^2=2^2.20^2=\left(2.20\right)^2=40^2\Rightarrow y=\pm40\)
\(\Rightarrow z^2=2^2.40^2=\left(2.40\right)^2=80^2\Rightarrow z=\pm80\)
5 tháng 1 2022
Câu 1:
=>5x=15
hay x=3
Câu 2:
\(\Leftrightarrow120-\left(3x+9\right)=12\)
=>3x+9=108
=>3x=99
hay x=33
23 tháng 7 2018
\(A=\frac{4^6x9^5+6^9x120}{8^4x3^{12}-6^{11}}\)
\(A=\frac{2^{12}x3^{10}+2^9x3^9x2^3x3x5}{2^{12}x3^{12}-2^{11}x3^{11}}\)
\(A=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{10}-2^{11}.3^{11}}\)
\(A=\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{10}.\left(2-3\right)}=\frac{2.6}{-1}=-12\)
13 tháng 7 2017
Đặt:
\(X=\left(1+\dfrac{1}{9}\right)\left(1+\dfrac{1}{10}\right)\left(1+\dfrac{1}{11}\right).....\left(1+\dfrac{1}{200}\right)\)
\(X=\dfrac{10}{9}.\dfrac{11}{10}.\dfrac{12}{11}......\dfrac{201}{200}\)
\(X=\dfrac{10.11.12......201}{9.10.11......200}\)
\(X=\dfrac{201}{9}\)
\(Y=\left(1-\dfrac{1}{10}\right)\left(1-\dfrac{1}{11}\right)\left(1-\dfrac{1}{12}\right).....\left(1-\dfrac{1}{99}\right)\)
\(Y=\dfrac{9}{10}.\dfrac{10}{11}.\dfrac{11}{12}.....\dfrac{98}{99}\)
\(Y=\dfrac{9.10.11......98}{10.11.12.....99}\)
\(Y=\dfrac{9}{99}=\dfrac{1}{11}\)
9x(12+X)=120
108+9X=120
9X=120-108
9X=12
X=12:9=4/3