The product of all the rational roots of the equation (x² - 9x + 11)² - (x - 4) (x - 5) = 3, is equal to:

The equation simplifies to (x^2 - 9x + 11)^2 - (x^2 - 9x + 20) = 3. Let u = x^2 - 9x. Then (u+11)^2 - (u+20) = 3, which expands to u^2 + 22u + 121 - u - 20 = 3, or u^2 + 21u + 98 = 0. Factoring gives (u+7)(u+14) = 0, so x^2 - 9x + 7 = 0 or x^2 - 9x + 14 = 0. The product of roots for the first is 7 and for the second is 14; however, checking the question phrasing, the product of all rational roots is 14 * 1 = 14.