TH1: m+n+p khác 0
\(\frac{m+n-p}{p}=\frac{n+p-m}{m}=\frac{p+m-n}{n}\)
\(\Rightarrow2+\frac{m+n-p}{p}=2+\frac{n+p-m}{m}=2+\frac{p+m-n}{n}\)
\(\Rightarrow\frac{m+n+p}{p}=\frac{n+p+m}{m}=\frac{p+m+n}{n}\)
\(\Rightarrow p=m=n\)
thay m=n=p vào biểu thức H ta có:
\(H=\left(1+\frac{m}{m}\right).\left(1+\frac{n}{n}\right).\left(1+\frac{p}{p}\right)\)
\(H=2.2.2=2^3=8\)
TH2: m+n+p = 0 (m,n,p khác 0)
=> m=-(n+p)
=> n=-(m+p)
=>p=-(n+m)
thay m=-(n+p), n=-(m+p), p=-(n+m) vào biểu thức H
\(H=\left(1+\frac{-m-p}{m}\right).\left(1+\frac{-n-m}{n}\right).\left(1+\frac{-n-p}{p}\right)\)
\(H=\left(-\frac{p}{m}\right).\left(-\frac{m}{n}\right).\left(\frac{-n}{p}\right)=-1\)
