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Consider also the following way

x, y, z = var("x, y, z")
def U(a, b): return sqrt(a)*sqrt(b)
def B(a, b): return a/16+b
p=plot3d(U, (0, 16), (0, 16), color="red") +\
plot3d(B, (0, 16), (-1, 16), color="blue",opacity=0.7) 
solve(U(x,y)^2==B(x,y)^2,y)

[y == -1/16*x*(4*sqrt(3) - 7), y == 1/16*x*(4*sqrt(3) + 7)]

sqr3=sqrt(3).n()
pp=[(x,1/16*x*(4*sqr3 + 7),sqrt(x)*sqrt(1/16*x*(4*sqr3 + 7)))
    for x in srange(0.0,16.0,1.0)]
p+=line3d(pp,color='yellow',radius=0.1)
pp1=[(x,-1/16*x*(4*sqr3 - 7),x/16-(1/16*x*(4*sqr3 - 7)))
    for x in srange(0.0,16.0,1.0)]
p+=line3d(pp1,color='yellow',radius=0.1)
p.rotateZ(pi/1.11).show(frame=False,aspect_ratio=[1,1,0.6])