1/ Ta có: \(\frac{y}{16}=\frac{-1}{4}\)
=> \(y.4=\left(-1\right).16=-16\)
=> \(y=\left(-16\right):4=-4\)
Có: \(\frac{-5}{x}=\frac{y}{16}\)
=> \(x.y=\left(-5\right).16=\left(-80\right)\)
Hay: \(x.\left(-4\right)=-80\)
=> \(x=\left(-80\right):\left(-4\right)=20\)
Vậy: y = -4; x = 20
2/
a. \(\frac{1717-101}{2828+404}=\frac{17.101-101.1}{28.101+4.101}=\frac{101.\left(17-1\right)}{101.\left(28+4\right)}=\frac{101.16}{101.32}=\frac{16}{32}=\frac{1}{2}\)
b. \(\frac{3^5.5^{11}}{5^{12}.3^2}=\frac{3^2.3^3.5^{11}}{5^{11}.5.3^2}=\frac{3^3}{5}=\frac{27}{5}\)
3/ Gọi d là ƯCLN (2n + 1; 3n +1)
Ta có: \(\left\{{}\begin{matrix}2n+1⋮d\\3n+1⋮d\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}6n+3⋮d\\6n+2⋮d\end{matrix}\right.\)
=> (6n + 3) - (6n + 2) ⋮d
=> 6n + 3 - 6n - 2 ⋮d
=> 1⋮d
=> d = 1
Hay: ƯCLN (2n + 1; 3n +1) = 1
=> Phân số \(\frac{2n+1}{3n+1}\) tối giản với mọi n ∈ Z
P/s: Mình giải hết cho bạn rồi đó!
\(\frac{-5}{x}=\frac{y}{16}=\frac{-1}{4}\)
\(\Leftrightarrow\left\{{}\begin{matrix}xy=-80\\4y=-16\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=20\\y=-4\end{matrix}\right.\)
