Given $x\neq0$, find the positive value of $b$ such that the equation 3/x + x/9 = b will have exactly one solution.
3/x + x/9 = b multiply through by x
3 + x^2/9 = bx rearrange as
(1/9)x^2 - bx + 3 = 0
If this has one solution , the discriminant = 0
So
b^2 - 4(1/9)(3) = 0
b^2 = 12/9
b^2 = 4/3 take the positive root
b = 2 / sqrt (3)
