Question

[LƯU THIÊN HƯƠNG]

Tìm các số nguyên x,y thoa man

a, (2x-1)² :9 =49

b. 3^x + 3^{x+ 2} = 810

c.80:x, 56:x va x l> hoac =3

d.\(\frac{2x}{3}-\frac{2}{y}=\frac{1}{3}\)

Answer 1

[Nhật Hạ]

a, \(\left(2x-1\right)^2:9=49\)

\(\left(2x-1\right)^2=441\)

\(\Rightarrow\orbr{\begin{cases}2x-1=441\\2x-1=-441\end{cases}\Rightarrow\orbr{\begin{cases}x=221\\x=-220\end{cases}}}\)

b, \(3^x+3^{x+2}=810\)

\(3^x+3^x.3^2=810\)

\(3^x\left(1+3^2\right)=810\)

\(3^x.10=810\)

\(3^x=81=3^4\)

\(\Rightarrow x=4\)

Answer 2

[Nhật Hạ]

\(\hept{\begin{cases}80⋮x\\56⋮x\end{cases}}\Rightarrow x\inƯC\left(80;56\right)\)

\(80=2^4.5\)

\(56=2^3.7\)

\(ƯCLN\left(80;56\right)=2^3=8\)

\(\RightarrowƯC\left(80;56\right)=Ư\left(8\right)=\left\{\pm1;\pm2;\pm4;\pm8\right\}\)

Mà \(x\ge3\)

\(\Rightarrow x\in\left\{4;8\right\}\)