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Ta có \(\dfrac{2}{1\cdot5}+\dfrac{2}{5\cdot9}+\dfrac{2}{9\cdot13}+...+\dfrac{2}{x\left(x+4\right)}=\dfrac{56}{113}\)
\(\dfrac{1}{2}\left(\dfrac{4}{1\cdot5}+\dfrac{4}{5\cdot9}+\dfrac{4}{9\cdot13}+...+\dfrac{4}{x\left(x+4\right)}\right)=\dfrac{56}{113}\)
\(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{x}-\dfrac{1}{x+4}=\dfrac{56}{113}:\dfrac{1}{2}\)
\(1-\dfrac{1}{x+4}=\dfrac{112}{113}\)
\(\dfrac{1}{x+4}=1-\dfrac{112}{113}=\dfrac{1}{113}\)
x + 4 = 113 ⇒ x = 109
\(\dfrac{2}{1.5}+\dfrac{2}{5.9}+...+\dfrac{2}{x\left(x+4\right)}=\dfrac{56}{113}\)
Xét: \(A=\dfrac{2}{1.5}+\dfrac{2}{5.9}+...+\dfrac{2}{x\left(x+4\right)}\)
\(A=\dfrac{1}{2}.\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{x-4}-\dfrac{1}{x}+\dfrac{1}{x}-\dfrac{1}{x+4}\right)\)
\(A=\dfrac{1}{2}.\left(1-\dfrac{1}{x+4}\right)\)
Với \(A=\dfrac{56}{113}\) thì
\(\dfrac{1}{2}.\left(1-\dfrac{1}{x+4}\right)=\dfrac{56}{113}\)
\(\left(1-\dfrac{1}{x+4}\right)=\dfrac{112}{113}\)
\(\dfrac{1}{x+4}=\dfrac{1}{113}\)
\(x=109\)
mới làm qua thôi chứ chưa biết có đúng ko:
Ta có:
3 - \(\frac{999999999}{6}\)= \(\frac{3}{1}\)- \(\frac{999999999}{6}\)=\(\frac{18}{6}\)- \(\frac{999999999}{6}\)= \(\frac{-999999981}{6}\)là một phân số âm
=> A= 999999999/2-999999999/-999999981/6 là một phân số âm
=> A < 0
kiểm tra lại cho mk luôn
`@` `\text {Ans}`
`\downarrow`
`[ (100 - x)*2 - 2] = 40`
`=> (100-x)*2 - 2 = 40`
`=> (100 - x)*2 = 40 + 2`
`=> (100 - x)*2 = 42`
`=> 100 - x = 42 \div 2`
`=> 100 - x = 21`
`=> x = 100 - 21`
`=> x = 79`
Vậy, `x=79.`
\(\left[\left(100-x\right).2-2\right]=40\)
\(=>\left(100-x\right).2=40+2\)
\(=>\left(100-x\right).2=42\)
\(=>100-x=42:2\)
\(=>100-x=21\)
\(=>x=100-21\)
\(=>x=79\)
Chúc bạn học tốt
a ) hông hiểu
b ) \(\frac{x}{5}=\frac{y}{3}=\frac{x+y}{5+3}=\frac{16}{8}=2\)
\(\Rightarrow\frac{x}{5}=2\Rightarrow x=2.5=10\)
\(\Rightarrow\frac{y}{3}=2\Rightarrow y=2.3=6\)
Vậy x = 10 ; x = 6
em moi hc lop 5,ma bai nayem hc roi thi nhat dinh em se giai cho
\(a,A=\frac{3}{2}+\frac{3}{6}+\frac{3}{12}+\frac{3}{20}+...+\frac{3}{90}\)
\(A=3.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\right)\)
\(A=3.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(A=3.\left(1-\frac{1}{10}\right)\)
\(A=3.\frac{9}{10}=\frac{27}{10}\)
\(b,B=\frac{2}{2.5}+\frac{2}{5.8}+\frac{2}{8.11}+\frac{2}{11.14}+\frac{2}{14.17}\)
\(B.\frac{3}{2}=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}+\frac{3}{14.17}\)
\(B.\frac{3}{2}=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}\)
\(B.\frac{3}{2}=\frac{1}{2}-\frac{1}{17}\)
\(B=\frac{15}{34}:\frac{3}{2}=\frac{5}{17}\)
\(\frac{x}{2}+\frac{3}{5}.\left(x-2\right)=3\)
\(\frac{x}{2}+\frac{3}{5}x-\frac{6}{5}=3\)
\(\frac{x}{2}+\frac{3x}{5}=\frac{21}{5}\)
\(\frac{11x}{10}=\frac{21}{5}\)
\(11x=42\)
\(x=\frac{42}{11}\)
Ta có: \(\frac{1}{2}x+\frac{3}{5}.\left(x-2\right)=3\)
\(\frac{1}{2}x+\frac{3}{5}x-\frac{6}{5}=3\)
\(\frac{11}{10}x=\frac{21}{5}\)
\(x=\frac{42}{11}\)
\(5x=6y\Leftrightarrow\frac{x}{6}=\frac{y}{5};x^2-y^3=11\)
Tính chất dãy tỉ số bằng nhau:
\(\frac{x}{6}=\frac{y}{5}=\frac{x^2-y^3}{6^2-5^3}=\frac{11}{-89}=-\frac{11}{89}\)
\(\Rightarrow\hept{\begin{cases}\frac{x}{6}=-\frac{11}{89}\Leftrightarrow x=\frac{-11.6}{89}=-\frac{66}{89}\\\frac{y}{5}=-\frac{11}{89}\Leftrightarrow y=\frac{-11.5}{89}=-\frac{55}{89}\end{cases}}\)
\(A.12:\left(x+4\right)=2\)
\(\Rightarrow x+4=12:2\)
\(\Rightarrow x+4=6\)
\(\Rightarrow x=2\)
\(B,12:\left(x+4\right).3+18=24\)
\(12:\left(x+4\right).3=6\)
\(\Rightarrow12:\left(x+4\right)=2\)
\(\Rightarrow x+4=6\)
\(\Rightarrow x=2\)
a) 12 : ( x + 4 ) = 2
x + 4 = 12 : 2
x + 4 = 6
x = 6 - 4
x = 2
Vậy x = 2
b) 12 : ( x + 4 ) . 3 + 18 = 24
12 : ( x + 4) . 3 = 24 - 18
12 : ( x + 4 ) . 3 = 6
12 : ( x + 4 ) = 6 : 3
12 : ( x + 4 ) = 2
x + 4 = 12 : 2
x + 4 = 6
x = 6 - 4
x = 2
Vậy x = 2
Học tốt !!!
=))
\(\frac{x-2}{2}=\frac{18}{x-2}\)
\(\Rightarrow\left(x-2\right)^2=18\times2\)
\(\Leftrightarrow\left(x-2\right)^2=36\)
\(\Leftrightarrow\left(x-2\right)^2=6^2\)
\(\Leftrightarrow\orbr{\begin{cases}x-2=-6\\x-2=6\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-4\\x=8\end{cases}}\)
Vậy \(x\in\left\{-4;8\right\}\)
\(\frac{x-2}{2}=\frac{18}{x-2}\)
\(\Rightarrow\left(x-2\right).\left(x-2\right)=18.2\)
\(\Rightarrow\left(x-2\right)^2=36\)
\(\Rightarrow\orbr{\begin{cases}x-2=6\\x-2=-6\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=8\\x=-4\end{cases}}\)
Vậy \(\orbr{\begin{cases}x=8\\x=-4\end{cases}}\)
Chúc bạn học tốt !!!