Question

The difference between two positive numbers is 4 and the difference between their cubes is 316.
Find : The sum of their squares

Answer 1

Given difference between two positive numbers is 4 and difference between their cubes is 316.
Let the positive numbers be a and b

a - b = 4                         .....(1)
a³ - b³ = 316              .....(2)

ab = 21                  .....(3)

Squaring(eq 1) both sides, we get

(a - b)² = 16

a² + b² - 2ab = 16

a² + b² = 2 × 21 + 16

a² + b² = 42 + 16

a² + b² = 58
Sum of their squares is 58.