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= \(\frac{1}{2}\). ( \(\frac{2}{1.3}\) + \(\frac{2}{3.5}\) + \(\frac{2}{5.7}\) ... + \(\frac{2}{x.\left(x+2\right)}\) )
= \(\frac{1}{2}\) . ( 1 - \(\frac{1}{3}\) + \(\frac{1}{3}\) - \(\frac{1}{5}\) + \(\frac{1}{5}\) - \(\frac{1}{7}\) + ... + \(\frac{1}{x}\)- \(\frac{1}{x+2}\) )
= ................
Bạn tự làm tiếp nhé ! Chúc bạn học tốt :)
Ta có : \(\frac{x}{-3}=\frac{4}{y}\)\(=x.y=-12\)
Và \(-12=-1.12=\left(-1\right).12=-2.6=\left(-2\right).6=-3.4=\left(-3\right).4\)
Ta có các cặp xy là :
\(\orbr{\begin{cases}x=-1\\y=12\end{cases}}\orbr{\begin{cases}x=\left(-1\right)\\y=12\end{cases}}\)
\(\orbr{\begin{cases}x=-2\\x=6\end{cases}}\orbr{\begin{cases}x=\left(-2\right)\\x=6\end{cases}}\)
\(\orbr{\begin{cases}x=-3\\y=4\end{cases}}\orbr{\begin{cases}x=\left(-3\right)\\y=4\end{cases}}\)
nguyễn nam dương :
mik thấy bạn làm hơi thừa nhưng bạn trả lời nên mik vẫn k cho nha
a/ \(\frac{x}{-3}=\frac{4}{y}\Rightarrow xy=-12\Rightarrow\left(x;y\right)\)
=> (x;y)={(-1;12), (1;-12), (-2;6), (2;-6), (-3;4), (3;-4)}
b/ \(\frac{-x}{4}=\frac{-9}{x}\Rightarrow x^2=36\Rightarrow x=\pm6\)
\(\frac{x+2}{17}+\frac{x+4}{15}+\frac{x+6}{13}=\frac{x+8}{11}+\frac{x+10}{9}+\frac{x+12}{7}\)
\(\Rightarrow\left(\frac{x+2}{17}+1\right)+\left(\frac{x+4}{15}+1\right)+\left(\frac{x+6}{13}+1\right)-\left(\frac{x+8}{11}+1\right)-\left(\frac{x+10}{9}+1\right)-\left(\frac{x+12}{7}+1\right)=0\)
\(\Rightarrow\frac{x+19}{17}+\frac{x+19}{15}+\frac{x+19}{13}-\frac{x+19}{11}-\frac{x+19}{10}-\frac{x+19}{7}=0\)
\(\Rightarrow\left(x+19\right)(\frac{1}{17}+\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}-\frac{1}{7})\)
\(\Rightarrow x+19=0\)\(\left(Vì\frac{1}{17}+\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}-\frac{1}{7}\ne0\right)\)
\(\Rightarrow x=-19\)
Ta có : \(\frac{x+2}{17}+\frac{x+4}{15}+\frac{x+6}{13}=\frac{x+8}{11}+\frac{x+10}{9}+\frac{x+12}{7}\)
\(\Rightarrow\left(\frac{x+2}{17}+1\right)+\left(\frac{x+4}{15}+1\right)+\left(\frac{x+6}{13}+1\right)=\left(\frac{x+8}{11}+1\right)+\left(\frac{x+10}{9}+1\right)+\left(\frac{x+12}{7}+1\right)\)
\(\Rightarrow\frac{x+19}{17}+\frac{x+19}{15}+\frac{x+19}{13}-\frac{x+19}{11}-\frac{x+19}{9}-\frac{x+19}{7}=0\)
\(\Rightarrow\left(x+19\right)\left(\frac{1}{17}+\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}-\frac{1}{7}\right)=0\)
\(\Rightarrow x+19=0\Rightarrow x=-19\)
Ta có:\(\frac{4}{x}=\frac{2}{x+4}\)
\(\Leftrightarrow4x+16=2x\)
\(\Leftrightarrow4x-2x=-16\)
\(\Leftrightarrow2x=-16\)
\(\Leftrightarrow x=-8\)
hok tốt!!