Câu 1:
\(M=132-\left\{100-\left[\left(78-73\right)^2:5+9\right]\right\}\)
\(=132-\left\{100-\left[5^2:5+9\right]\right\}\)
\(=132-100+5+9\)
=32+14
=46
Câu 2:
105-[(2x+7)-13]=25
=>(2x+7)-13=105-25=90
=>2x-6=90
=>2x=96
=>x=96/2=48
Câu 4:
\(N=\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+...+\dfrac{1}{99\cdot101}\)
\(=\dfrac{1}{2}\cdot\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{99\cdot101}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{101}\right)=\dfrac{1}{2}\cdot\dfrac{100}{101}=\dfrac{50}{101}\)
Câu 5:
\(xy-x+2y=3\)
\(\Rightarrow xy-x+2y-2=3-2\)
\(\Rightarrow\left(xy-x\right)+\left(2y-2\right)=1\)
\(\Rightarrow x\left(y-1\right)+2\left(y-1\right)=1\)
\(\Rightarrow\left(x+2\right)\left(y-1\right)=1\)
Ta có bảng sau:
| \(x+2\) | \(1\) | \(-1\) |
| \(y-1\) | \(1\) | \(-1\) |
| \(x\) | \(-1\) | \(-3\) |
| \(y\) | \(2\) | \(0\) |
Vậy các cặp (x;y) là (-1;2) ; (-3;0)
#YM
