The sum of two positive numbers is 14 and difference between their squares is 56. What is the sum of their squares?

Let the numbers be a and b,

⇒ a + b = 14 ---- (1)

⇒ a2 – b2 = 56 ---- (2)

We know that (a2 – b2) = (a + b) (a – b)

⇒ (a + b) (a – b) = 56

Since (a + b) = 14

⇒ (a – b) = 4 ---- (3)

Solving equations 1 and 2,

⇒ a = 9 and b = 5

∴ Sum of squares = 81 + 25 = 106