Question

Cho phân số : A= 4/(n-2).(n+1). Hãy tìm n để phân số A = 1/7

Answer 1

\(L=\dfrac{4}{\left(n-2\right)\left(n+1\right)}=\dfrac{1}{7}\)

\(\Leftrightarrow\left(n-2\right)\left(n+1\right)=28\)

\(\Rightarrow n^2+n-2n-2=28\)

\(\Rightarrow n^2-n=30\)

\(\Rightarrow n^2-n+\dfrac{1}{4}=\dfrac{121}{4}\)

\(\Rightarrow\left(n-\dfrac{1}{2}\right)^2-\dfrac{121}{4}=0\)

\(\Rightarrow\left(n-\dfrac{1}{2}-\dfrac{11}{2}\right)\left(n-\dfrac{1}{2}+\dfrac{11}{2}\right)=0\)

\(\Rightarrow\left(n-6\right)\left(n+5\right)=0\Leftrightarrow\left[{}\begin{matrix}n=6\\n=-5\end{matrix}\right.\)