Gọi d là ƯCLN\((2n-3,3n-5)\)\((d\inℕ^∗)\)
Ta có : \(\hept{\begin{cases}2n-3⋮d\\3n-5⋮d\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}3(2n-3)⋮d\\2(3n-5)⋮d\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}6n-9⋮d\\6n-10⋮d\end{cases}}\)
\(\Rightarrow(6n-10)-(6n-9)⋮d\)
\(\Rightarrow1⋮d\)
\(\Rightarrow d=1\)
Vậy : ....
a,Tự làm đi bạn nhé
b, \(\frac{x}{4}=\frac{5}{y}\)
\(\Rightarrow x\cdot y=63=1\cdot63=63\cdot1=(-1)(-63)=(-63)(-1)\)
Vậy :....
\(c)\frac{x}{6}=\frac{3}{y}\)
\(\Rightarrow xy=3\cdot6\)
\(\Rightarrow xy=18\)
Tự lập bảng :>
\(\text{a) Gọi d = ƯCLN( 2n - 3 , 3n - 5 )}\)
\(\Rightarrow\hept{\begin{cases}2n-3⋮d\\3n-5⋮d\end{cases}}\Rightarrow\hept{\begin{cases}3\left(2n-3\right)⋮d\\2\left(3n-5\right)⋮d\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}6n-9⋮d\\6n-10⋮d\end{cases}}\Rightarrow\left(6n-10\right)-\left(6n-9\right)⋮d\)
\(\Rightarrow1⋮d\)
\(\Rightarrow d=1\)
\(\Rightarrow\text{ Phân số }\frac{2n-3}{3n-5}\text{ là 1 phân số tối giản}\)
\(\text{a) }\frac{x+1}{4}=\frac{9}{x+1}\)
\(\Rightarrow\left(x+1\right).\left(x+1\right)=4.9\)
\(\Rightarrow\left(x+1\right)^2=36\)
\(\Rightarrow\left(x+1\right)^2=6^2\)
\(\Rightarrow x+1=6\)
\(\Rightarrow x=5\)
\(\text{b) }\frac{x}{4}=\frac{5}{y}\)
\(\Rightarrow x.y=4.5\)
\(\Rightarrow x.y=20\)
\(\Rightarrow x,y\inƯ\left(20\right)\)
\(\Rightarrow x,y\in\left\{1;2;4;5;10;20\right\}\)
\(\Rightarrow x.y=\left\{1.20\right\};\left\{2.10\right\};\left\{4.5\right\}\)
\(\text{c) }\frac{x}{6}=\frac{3}{y}\)
\(\Rightarrow x.y=3.6\)
\(\Rightarrow x.y=18\)
\(\Rightarrow x,y\inƯ\left(18\right)\)
\(\Rightarrow x,y\in\left\{1;2;3;6;9;18\right\}\)
Ta có bảng giá trị
| x | 18 | 9 | 6 |
| y | 1 | 2 | 3 |
