Bài 2:
5.A=5+5^2+5^3+...+5^40
5.A-A=(5+5^2+5^3+...+5^40)-(1+5+5^2+...+5^39)
4.A=5^40-1
A=5^40-1/4
chúc bạn học tốt nha, câu 1 mk đang tính, xong mk gửi qua tin nhắn cho bạn nha
\(A=1+5+5^2+...+5^{39}\)
\(5A=5+5^2+5^3+...+5^{40}\)
\(5A-A=4A=\left(5+5^2+5^3+...+5^{40}\right)-\left(1+5+5^2+5^3+...+5^{49}\right)\)
\(4A=5^{40}-1\)
\(A=\frac{5^{40}-1}{4}\)
Bài 1 :
\(xy=2\left(x+y\right)\)
\(\Leftrightarrow\)\(2x+2y-xy=0\)
\(\Leftrightarrow\)\(\left(2x-xy\right)-\left(4-2y\right)=-4\)
\(\Leftrightarrow\)\(x\left(2-y\right)-2\left(2-y\right)=-4\)
\(\Leftrightarrow\)\(\left(x-2\right)\left(2-y\right)=-4\)
Ta có bảng :
| \(x-2\) | \(1\) | \(-1\) | \(2\) | \(-2\) | \(4\) | \(-4\) |
| \(2-y\) | \(-4\) | \(4\) | \(-2\) | \(2\) | \(-1\) | \(1\) |
| \(x\) | \(3\) | \(1\) | \(4\) | \(0\) | \(6\) | \(-2\) |
| \(y\) | \(6\) | \(-2\) | \(4\) | \(0\) | \(3\) | \(1\) |
Vậy \(\left(x,y\right)\in\left\{\left(3;6\right),\left(1;-2\right),\left(4;4\right),\left(0;0\right),\left(6;3\right),\left(-2;1\right)\right\}\)
Chúc bạn học tốt ~
