Question

[Đỗ Uyên Nhi]

cho m^2-2n^2=mn ( m khác 0,m+n khác 0). Tính A=m-n/m+n

Mk đang cần gấp nha

cảm ơn mn!

Answer 1

[Nobi Nobita]

Ta có: \(m^2-2n^2=mn\)

\(\Leftrightarrow m^2-2n^2-mn=0\)

\(\Leftrightarrow m^2-n^2-n^2-mn=0\)

\(\Leftrightarrow\left(m^2-n^2\right)-\left(n^2-mn\right)=0\)

\(\Leftrightarrow\left(m-n\right)\left(m+n\right)-n\left(n-m\right)=0\)

\(\Leftrightarrow\left(m-n\right)\left(m+n\right)+n\left(m-n\right)=0\)

\(\Leftrightarrow\left(m-n\right)\left(m+n+n\right)=0\)

\(\Leftrightarrow\left(m-n\right)\left(m+2n\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}m-n=0\\m+2n=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}m=n\\m=-2n\end{cases}}\)

TH1: Nếu \(m=n\)\(\Rightarrow m-n=0\)\(\Rightarrow A=\frac{m-n}{m+n}=0\)

TH2: Nếu \(m=-2n\)\(\Rightarrow A=\frac{-2n-n}{-2n+n}=\frac{-3n}{-n}=3\)

Vậy nếu \(m=n\)thì \(A=0\)

       nếu \(m=-2n\)thì \(A=3\)