In each of these questions, two equations (a) and (b) are given. You have to solve both the equations and choose the correct option. a) (x^2 – 13.5x + 38 = 0) b) (y^2 – 1.5y – 10 = 0)

Solve equation (a): x² - 13.5x + 38 = 0. Using quadratic formula or factoring: x = (13.5 ± √(13.5² - 4×38))/2 = (13.5 ± √(182.25 - 152))/2 = (13.5 ± √30.25)/2 = (13.5 ± 5.5)/2. So x = 19/2 = 9.5 or x = 8/2 = 4. Solve equation (b): y² - 1.5y - 10 = 0 gives y = (1.5 ± √(2.25 + 40))/2 = (1.5 ± √42.25)/2 = (1.5 ± 6.5)/2. So y = 8/2 = 4 or y = -5/2 = -2.5. All x values (9.5, 4) are greater than or equal to all y values (4, -2.5). Since x=4 and y=4 is possible (x=y) and x=9.5 > all y values, x ≥ y is correct.