In the following question two equations are given. You have to solve these equations and determine relation between x and y.
I. x2 – 12x + 35 = 0
II. y2 – 16y + 63 = 0
I. x2 – 12x + 35 = 0
⇒ x2 – 5x – 7x + 35 = 0
⇒ x(x – 5) – 7(x – 5) = 0
⇒ (x – 7) (x – 5) = 0
⇒ x = 7 OR x = 5
II. y2 – 16y + 63 = 0
⇒ y2 – 7y – 9y + 63 = 0
⇒ y (y – 7) – 9(y – 7) = 0
⇒ (y – 9) (y – 7) = 0
⇒ y = 9 OR y = 7
So, when x = + 7, x = y when y = 7 and x < y when y = 9.
And when x = 5, x < y when y = 7 and x < y when y = 9.
∴ x ≤ y.