The sum of two whole numbers is 7 and the sum of their cubes is 133, find the sum of their squares.

Let two numbers be x and y.

Given,

The sum of two whole numbers is 7 and the sum of their cubes is 133.

x + y = 7 and x³ + y³ = 133

By formula,

⇒ x³ + y³ = (x + y)³ - 3xy(x + y)

⇒ 133 = 7³ - 3xy × 7

⇒ 133 = 343 - 21xy

⇒ 21xy = 343 - 133

⇒ 21xy = 210

⇒ xy = 10.

By formula,

⇒ (x + y)² = x² + y² + 2xy

⇒ 7² = x² + y² + 2 × 10

⇒ 49 = x² + y² + 20

⇒ x² + y² = 49 - 20

⇒ x² + y² = 29.

Hence, sum of squares of numbers = 29.