\(\frac{a^2+2b^2-m^2}{a^2+3b^2-6m^2}=\frac{\left(4m\right)^2+2\left(5m\right)^2-m^2}{\left(4m\right)^2+3\left(5m\right)^2-6m^2}=\frac{16m^2+50m^2-m^2}{16m^2+375m^2-6m^2}\)
\(=\frac{65m^2}{385m^2}=\frac{13}{77}\)
thay a = 4m, b = 5m vào biểu thức trên ta được :
\(\frac{\left(4m\right)^2+2.\left(5m\right)^2-m^2}{\left(4m\right)^2+3.\left(5m\right)^2-6m^2}\)
\(=\frac{16m^2+50m^2-m^2}{16m^2+75m^2-6m^2}\)
\(=\frac{m^2.\left(16+50-1\right)}{m^2.\left(16+75-6\right)}\)
\(=\frac{65m^2}{85m^2}=\frac{65}{85}=\frac{13}{17}\)
Ta có :\(\frac{a^2+2b^2-m^2}{a^2+3b^2-6m^2}\)
Thay a = 4m ; b = 5m vào ta có :
\(=\frac{\left(4m\right)^2+2\left(5m\right)^2-m^2}{\left(4m\right)^2+3\left(5m\right)^2-6m^2}\)
\(=\frac{4^2.m^2+2.5^2.m^2-m^2}{4^2m^2+3.5^2m^2-6m^2}\)
\(=\frac{m^2\left(16+50-1\right)}{m^2\left(16+75-6\right)}=\frac{65}{85}=\frac{13}{17}\)
