If the sum of two numbers is 11 and sum of their cubes is 737, find the sum of their squares.

Let two numbers be a and b then according to question,

a + b = 11 and a³ + b³ = 737.

Cubing both sides of a + b = 11,

⇒ (a + b)³ = (11)³

⇒ a³ + b³ + 3ab(a + b) = 1331

⇒ 737 + 3ab(11) = 1331

⇒ 33ab = 1331 - 737

⇒ 33ab = 594

⇒ ab = 18.

We know that,

a² + b² = (a + b)² - 2ab

Substituting values we get,

⇒ a² + b² = (11)² - 2(18) = 121 - 36 = 85.

Hence, sum of squares of two numbers = 85.