[TEX]x+\frac{1}{x}+y+\frac{1}{y}=5[/TEX]
[TEX](x+y).(1+\frac{1}{x.y})=5[/TEX]
mà
[TEX]x^3+\frac{1}{x^3}+y^3+\frac{1}{y^3}=15.m-10[/TEX]
[TEX](x^3+y^3).(\frac{1}{x^3.y^3}+1)=15.m-10[/TEX]
[TEX](x+y).(x^2+y^2-x.y).(1+\frac{1}{x.y}).(1+\frac{1}{x^2.y^2}-\frac{1}{x.y})=15.m-10[/TEX]
[TEX]5.(x^2+y^2-x.y).(1+\frac{1}{x^2.y^2}-\frac{1}{x.y})=15.m-10[/TEX]
[TEX][(x+y)^2-3.x.y].[(1+\frac{1}{x.y})^2-\frac{3}{x.y}]=3.m-2[/TEX]
[TEX]25-\frac{3.(x+y)^2}{x.y}-3.x.y.(1+\frac{1}{x.y})^2-\frac{9.x.y}{x.y}=3.m-2[/TEX]
[TEX]16-\frac{3.(x+y)^2}{x.y}-\frac{3.(x.y+1)^2}{x.y}=3.m-2[/TEX]
[TEX](6-m).x.y=(x+y)^2-(x.y+1)^2[/TEX]
[TEX](6-m).x.y=(\frac{5.x.y}{1+x.y})^2-(x.y+1)^2[/TEX]
[TEX](6-m).x.y.(1+x.y)^2=25.x^2.y^2-(x.y+1)^4[/TEX]