Bài 27. Tìm \(x,y\) \(\left(x,y\in N\right)\) biết: \(\dfrac{1}{x}+\dfrac{y}{3}=\dfrac{5}{6}\)
Bài 30. Tìm \(x\) biết: \(\left(\dfrac{1}{5}+\dfrac{1}{5^2}+\dfrac{1}{5^3}+...+\dfrac{1}{5^6}\right):x=-25\)
Bài 32. Tìm \(n\in Z\) để các PS sau đạt GTNN
a) \(A=\dfrac{6n-4}{2n+3}\)
b) \(B=\dfrac{6n-1}{3n+2}\)
c) \(C=\dfrac{n-13}{n+3}\)
Bài 33. Tìm \(n\in Z\) để các PS sau đạt GTLN
a) \(M=\dfrac{5x-19}{x-9}\)
b) \(N=\dfrac{-3}{2x-5}\)
c) \(P=\dfrac{3n-1}{-2n+3}\)
Bài 35. Cho \(a,b,n\in N\)*.
So sánh \(\dfrac{a}{b}\) và \(\dfrac{a+n}{b+n}\)
Bài 36. So sánh \(P=\dfrac{n+1}{n+2}\) với \(G=\dfrac{n+2}{n+3}\)
Bài 36:
\(P=\dfrac{n+1}{n+2}=\dfrac{n+2-1}{n+2}=1-\dfrac{1}{n+2}\)
\(G=\dfrac{n+2}{n+3}=\dfrac{n+3-1}{n+3}=1-\dfrac{1}{n+3}\)
Ta có n+2<n+3
=>\(\dfrac{1}{n+2}>\dfrac{1}{n+3}\)
=>\(-\dfrac{1}{n+2}< -\dfrac{1}{n+3}\)
=>\(-\dfrac{1}{n+2}+1< -\dfrac{1}{n+3}+1\)
=>P<G
Bài 33:
a: \(M=\dfrac{5x-19}{x-9}=\dfrac{5x-45+26}{x-9}=5+\dfrac{26}{x-9}\)
Để M max thì x-9=1
=>x=10
b: \(N=\dfrac{-3}{2x-5}\)
Để N max thì 2x-5=-1
=>2x=4
=>x=2
c: \(P=\dfrac{3n-1}{-2n+3}=\dfrac{-3n+1}{2n-3}=\dfrac{1}{2}\cdot\dfrac{-6n+2}{2n-3}\)
\(=\dfrac{1}{2}\left(\dfrac{-6n+9-7}{2n-3}\right)\)
\(=\dfrac{1}{2}\left(-3-\dfrac{7}{2n-3}\right)\)
Để P max thì \(-3-\dfrac{7}{2n-3}\) max
=>\(3+\dfrac{7}{2n-3}\) min
=>2n-3=-1
=>2n=2
=>n=1