设x为实数,且满足等式x/2+1/2x=cost,求t

Question

设x为实数,且满足等式x/2+1/2x=cost,求t

Answer 1

x>0时,cos(t)=x/2+1/(2x)>=2(x/2)[1/(2x)]=1,cos(t)=1,t=2nπ.
x=2(-x/2)[1/(-2x)] = 1,cos(t)=-1,t=(2n+1)π.
综合,有,t=nπ,n=0,1,-1,2,-2,...