Question

（P）若实数m,n满足等式m²=7-3n,n²=7-3m,则代数式（n/m）+（m/n)的值是多少

Answer 1

m²=7-3n,n²=7-3m

即m,n是方程x^2+3x-7=0的二个不等的根,则有

m+n=-3,mn=-7

n/m+m/n=(n^2+m^2)/mn=[(m+n)^2-2mn]/mn=[9+14]/(-7)=-23/7