720 : ( a *2 + a*3) =2*3
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\(a.5+a=360:6\)
\(a\left(5+1\right)=60\)
\(a.6=60\)
\(a=\frac{60}{6}\)
Vậy\(a=10\)
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\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+100\right)=5750\)
\(\left(x+x+x+...+x\right)+\left(1+2+3+...+100\right)=5750\)
\(\Rightarrow100x+5050=5750\Rightarrow x=5750-5050\)
\(100x=700\Rightarrow x=700:100=7\)
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\(\frac{3}{a+b\sqrt{3}}-\frac{2}{a-b\sqrt{3}}=720\sqrt{3}\)
<=> \(a-5b\sqrt{3}=720\sqrt{3}\left(a^2-3b^2\right)\)
<=> \(a=\sqrt{3}\left(5b+720a^2-2160b^2\right)\)
Do a ,b là số hữu tỉ
=> \(a=5b+720a^2-2160b^2=0\)
=> \(\hept{\begin{cases}a=0\\5b-2160b^2=0\end{cases}}\)
Mà a,b không đồng thời bằng 0
=> \(a=0;b=\frac{1}{432}\)
Vậy \(a=0;b=\frac{1}{432}\)
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Chỉ làm bài khó thôi nhé:::::::::::::::
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x.\left(x+1\right)}=\frac{2016}{2018}\)
\(\Rightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+....+\frac{2}{x.\left(x+1\right)}=\frac{2016}{2018}\)
\(\Rightarrow2.\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{2016}{2018}\)
\(\Rightarrow\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x.\left(x+1\right)}=\frac{1013}{2018}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{1013}{2018}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{1013}{2018}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{2018}\Rightarrow x+1=2018\Rightarrow x=2017\)
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Ta có \(720\div\left(a\times2+a\times3\right)=2\times3\)
\(\Rightarrow720\div\left(5\times a\right)=6\)
\(\Rightarrow5\times a=720\div6\)
\(\Rightarrow5\times a=120\)
\(\Rightarrow a=120\div5\)
\(\Rightarrow a=24\)
720:(a*2+a*3)=6
a*2+a*3=720:6
a*2+a*3=120
a*5=120
a=120:5
a=24