Question

1. Cho \(N = 0,7.(2007^{2009}-2013^{1999}) \) . Chứng minh rằng : N là một số nguyên .

2. Tìm x , y biết :

a, \(\dfrac{x-1}{-15}=\dfrac{-60}{x-1}\)

b, \(\dfrac{2x+1}{5}=\dfrac{3y-2}{7}=\dfrac{2x+3y-1}{6x}\)

PLEASE HELP ME!!

Answer 1

\(\frac{x-1}{-15}=\frac{-60}{x-1}\)

\(\Leftrightarrow\left(x-1\right)^2=900\\ \Leftrightarrow\left(x-1\right)^2=\left(\pm30\right)^2\\ \Rightarrow x-1\in\left\{30;-30\right\}\)

\(\Rightarrow\left[{}\begin{matrix}x-1=30\\x-1=-30\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=31\\x=-29\end{matrix}\right.\)

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