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![](https://rs.olm.vn/images/avt/0.png?1311)
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)
1) K = D. 10 000 + Q
=> K-Q = D.10 000
=> 2015(K-Q) + 2016D = 2015.D.10 000 + 2016D =20152016.D
Vậy 2015(K-Q) + 2016D chia cho D = 20152016D:D = 20152016
2) \(A=\frac{\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}\right)}{\frac{1}{4}+\frac{1}{5}+\frac{1}{6}}=\)
\(A=\frac{\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}\right)-\left(1+\frac{1}{2}+\frac{1}{3}\right)}{\frac{1}{4}+\frac{1}{5}+\frac{1}{6}}=\)
\(=\frac{\frac{1}{4}+\frac{1}{5}+\frac{1}{6}}{\frac{1}{4}+\frac{1}{5}+\frac{1}{6}}=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
b1:<=>(x2-4x+4)y-3x2+12x-12=-4
=>(x2-4x+4)y-3x2+12x-(-4)-12=0
=>(x2-4x+4)y-3x2+12x-8=0
=>x2-4x+4=0
ta có (-4)2-4(1.4)=0
\(\Rightarrow x_{1,2}=\frac{b\pm\sqrt{\Delta}}{2a}=\frac{4\pm\sqrt{0}}{2}\)
=>x=2
thay x=2 vào rồi tìm y
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\right).x=\frac{23}{45}\)
\(\frac{1}{2}.\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+...+\frac{10-8}{8.9.10}\right).x=\frac{23}{45}\)
\(\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right).x=\frac{23}{45}:\frac{1}{2}\)
\(\left(\frac{1}{2}-\frac{1}{9.10}\right).x=\frac{46}{45}\)
\(\frac{22}{45}.x=\frac{46}{45}\)
\(x=\frac{46}{45}:\frac{22}{45}\)
\(x=\frac{23}{11}\)
\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+....+\frac{1}{8.9.10}\right).x=\frac{23}{45}\)
Ta có:\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}=\frac{1}{2}\cdot\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right)=\frac{1}{2}\cdot\left(\frac{1}{2}-\frac{1}{9.10}\right)=\frac{1}{2}\cdot\frac{22}{45}=\frac{11}{45}\)
=>\(\frac{11}{45}\cdot x=\frac{23}{45}\)
=>11x=23
=>x=23/11