设a^(1/2)-a^(-1/2)=m,则(a²+1)/a等于多少

Question

设a^(1/2)-a^(-1/2)=m,则(a²+1)/a等于多少

Answer 1

令t=a^(1/2),则a=t^2
t-1/t=m,(a^2+1)/a=a+1/a=t^2+1/t^2=(t-1/t)^2+2=m^2+2