t) 53 . 51 + 4 + 53 . 49 + 91 + 53
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1 :
a) \(xy-2x+2y=10\)
\(\Leftrightarrow x\left(y-2\right)+2y=10\)
\(\Leftrightarrow x\left(y-2\right)+2y-4=6\)
\(\Leftrightarrow x\left(y-2\right)+2\left(y-2\right)=6\)
\(\Leftrightarrow\left(x+2\right)\left(y-2\right)=6\)
Ta có : \(x+2\ge2\) vì \(x\in N\)
Do đó : ta có bảng :
x+2 : 2 3 6
y-2 : 3 2 1
x : 0 1 4
y : 5 4 3
Vậy...........
a) \(xy-2x+2y=10\left(x;y\inℕ\right)\)
\(\Rightarrow2xy-4x+4y=20\)
\(\Rightarrow2x\left(y-2\right)+4y-8+8=20\)
\(\Rightarrow2x\left(y-2\right)+4\left(y-2\right)=12\)
\(\Rightarrow\left(2x+4\right)\left(y-2\right)=12\)
\(\Rightarrow\left(2x+4\right);\left(y-2\right)\in\left\{1;2;3;4;6;12\right\}\)
\(\Rightarrow\left(x;y\right)\in\left\{\left(-\dfrac{3}{2};14\right);\left(-1;8\right);\left(-\dfrac{1}{3};6\right);\left(0;5\right);\left(1;3\right);\left(4;3\right)\right\}\)
\(\Rightarrow\left(x;y\right)\in\left\{\left(0;5\right);\left(1;3\right);\left(4;3\right)\right\}\left(x;y\inℕ\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\text{13.58.4+32.26.2+52.10}\)
\(\text{=(13.4).58 + (26.2)32 + 52.10}\)
\(\text{=52.58+52.32+52.10}\)
\(\text{=52(58+32+10)}\)
\(\text{=52.100}\)
\(\text{= 5200}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(3^x+3^{x+1}+3^{x+2}=117\)
\(3^x+3^x.3+3^x.3^2=117\)
\(3^x\left(1+3+3^2\right)=117\)
\(3^x.13=117\)
\(3^x=9\)
\(\Rightarrow x=2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(8.9.14+6.17.12+19.4.18\)
\(=4.2.9.14+6.3.17.4+19.4.18\)
\(=4.18.14+18.4.17+19.4.18\)
\(=4.18.\left(14+17+19\right)\)
\(=4.18.50\)
\(=3600\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Kết quả thì lớn lắm hay bạn muốn biến đổi nó như thế nào
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(2^{x+1}-2^x=32\)
\(\Rightarrow2^x\left(2-1\right)=2^5\)
\(\Rightarrow2^x.1=2^5\)
\(\Rightarrow x=5\)
b) \(2^{x+1}=2\)
\(\Rightarrow2^{x+1}=2^1\)
\(\Rightarrow x+1=1\)
\(\Rightarrow x=0\)
\(2^{x+1}-2^x=32\)
\(2^x.2-2^x=32\)
\(2^x\left(2-1\right)=32\)
\(2^x=32\)
\(x=5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\overline{abc}=100a+10b+c=a+b+c+263\)
\(\Rightarrow99a+9b=263\)
\(\Rightarrow9\left(11a+b\right)=263\)
mà \(263\) là số nguyên tố
Nên không tồn tại \(\left(a;b\right)\) thỏa đề bài.
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
\(206=2\cdot103\\ 540=2^2\cdot3^3\cdot5\)
Vậy ƯCLN của 206 và 540 là 2.
\(53.51+4+53.49+91+53\)
\(=53.\left(51+49+1\right)+4+91\)
\(=53.101+4+91\)
\(=5353+4+91\)
\(=5448\)
cảm ơn