Which smallest positive number should be subtracted from each of 9 and 13 so that 18 is the third proportion to them?

1

Let the required number be x 

Then, 9 - x : 13 - x :: 13 - x : 18

         18  = \(\frac{(13-x)²}{9-x}\)

18(9 - x)  = (13 - x)²

162 - 18x = x² - 26x + 169

 x² - 8x + 7 = 0

Solving,

x = 1, 7

smallest positive number is 1