\(3\frac{2}{9}-(1\frac{5}{9}+1\frac{2}{9})\text{=}\)
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theo bài ra ta có
n = 8a +7=31b +28
=> (n-7)/8 = a
b= (n-28)/31
a - 4b = (-n +679)/248 = (-n +183)/248 + 2
vì a ,4b nguyên nên a-4b nguyên => (-n +183)/248 nguyên
=> -n + 183 = 248d => n = 183 - 248d (vì n >0 => d<=0 và d nguyên )
=> n = 183 - 248d (với d là số nguyên <=0)
vì n có 3 chữ số lớn nhất => n<=999 => d>= -3 => d = -3
=> n = 927
![](https://rs.olm.vn/images/avt/0.png?1311)
cái dấu trước dấu chia mình ko biết cách đóng ngoặc nhọn lại nên mình viết như vậy
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{98.99.100}\)
= \(\frac{1}{2}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{98.99.100}\right)\)
= \(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{98.99}-\frac{1}{99.100}\right)\)
= \(\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{99.100}\right)=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{9900}\right)=\frac{1}{2}.\frac{4949}{9900}=\frac{4949}{19800}\left(\text{đpcm}\right)\)
\(VT=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{98.99.100}\)
\(=\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{98.99.100}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{98.99}-\frac{1}{99.100}\right)\)
\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{99.100}\right)=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{9900}\right)=\frac{1}{2}.\frac{4949}{9900}=\frac{4949}{19800}=VP\) (đpcm)
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1. \(\frac{5}{9}.\frac{7}{13}+\frac{5}{9}.\frac{9}{13}-\frac{5}{9}.\frac{3}{13}\)
= \(\frac{5}{9}\) .(\(\frac{7}{13}+\frac{9}{13}-\frac{3}{13}\) )
= \(\frac{5}{9}\) . 1 = \(\frac{5}{9}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{4}{5}-\left|3-x\right|=\frac{1}{4}\)
\(\Rightarrow\left|3-x\right|=\frac{4}{5}-\frac{1}{4}\)
\(\Rightarrow\left|3-x\right|=\frac{11}{20}\)
\(\Rightarrow\hept{\begin{cases}3-x=\frac{11}{20}\\3-x=-\frac{11}{20}\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=\frac{49}{20}\\x=\frac{71}{20}\end{cases}}\)
\(\frac{8}{9}:x^2+\frac{1}{9}=1\)
\(\Rightarrow\frac{8}{9}:x^2+\frac{1}{9}=\frac{9}{9}\)
\(\Rightarrow\frac{8}{9}:x^2=\frac{9}{9}-\frac{1}{9}\)
\(\Rightarrow\frac{8}{9}:x^2=\frac{8}{9}\)
\(\Rightarrow x^2=\frac{8}{9}:\frac{8}{9}\)
\(\Rightarrow x^2=1\)
\(\Rightarrow x^2=1^2\)
\(\Rightarrow x=1\)
Thêm:
\(\frac{4}{5}+\frac{3}{4}.x\frac{5}{2}\)
\(x-\frac{1}{2}=-\frac{5}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a)\(\frac{11^4.6-11^5}{11^4-11^5}:\frac{9^8.3-9^9}{9^8.5+9^8.7}\)
\(=1.6:\frac{9^8.3-9^8.9}{9^8.\left(5+7\right)}\)
\(=6:\frac{9^8.\left(3-9\right)}{9^8.12}\)
\(=6:\frac{9^8.\left(-6\right)}{9^8.12}\)
\(=6:\left(-\frac{6}{12}\right)\)
\(=6:\left(-\frac{1}{2}\right)\)
\(=-12\)
b) 3/5 : ( -1/5-1/6)+3/5:(-1/3-16/15) ( mình chuyển về ps luôn )
=3/5: (-11/30) + 3/5 : (-7/5)
=3/5:[-11/30+(-7/5)]
=3/5:53/30
=18/53
c) (1/2-13/14):5/7-(-2/21+1/7):5/7
= -3/7:5/7-1/21:5/7
=(-3/7-1/21):5/7
=-10/21:5/7
=-2/3
câu b vá c mình làm tắt nha. chúc bạn học tốt
\(=3\frac{2}{9}-2\frac{7}{9}=\frac{29}{9}-\frac{25}{9}=\frac{4}{9}\)
Chúc bạn học tốt!!!
\(3\frac{2}{9}\)\(-\left(1\frac{5}{9}+1\frac{2}{9}\right)\)
= \(\frac{29}{9}\)\(-\left(\frac{14}{9}+\frac{11}{9}\right)\)
= \(\frac{29}{9}\)\(-\frac{25}{9}\)
= \(\frac{4}{9}\)