\(\frac{a^2+2b^2-m^2}{a^2+3b^2-6m^2}\)
\(=\frac{\left(4m\right)^2+2\times\left(5m\right)^2-m^2}{\left(4m\right)^2+3\times\left(5m\right)^2-6m^2}\)
\(=\frac{16m^2+2\times25m^2-m^2}{16m^2+3\times25m^2-6m^2}\)
\(=\frac{15m^2+50m^2}{10m^2+75m^2}\)
\(=\frac{65m^2}{85m^2}\)
\(=\frac{13}{17}\)
cách giải :
Ta có :
a = 4m ; b = 5m
Thay vào biểu thức , ta có :
\(\frac{a^2+2b^2-m^2}{a^2+3b^2-6m^2}=\frac{\left(4m\right)^2+2\left(5m\right)^2-m^2}{\left(4m\right)^2+3\left(5m\right)^2-6m^2}=\frac{16.m^2+2.25.m^2-1.m^2}{16m^2+3.25.m^2-6.m^2}=\frac{\left(16+50-1\right)m^2}{\left(16+75-6\right)m^2}=\frac{65}{85}=\frac{13}{17}\)