Question

The sum of two numbers is 5 and the sum of their cubes is 35. Find the product of the numbers.

Answer 1

Given:

• The sum of two numbers x and y is 5, i.e., x + y = 5.
• The sum of their cubes is 35, x³ + y³ = 35.

Step-wise calculation:

1. Start with the identity for the sum of cubes:

x³ + y³ = (x + y)³ – 3xy(x + y)

2. Substitute x + y = 5: 

x³ + y³ = 5³ – 3xy × 5

x³ + y³ = 125 – 15xy 

3. Since x³ + y³ = 35, equate and solve for xy: 

35 = 125 – 15xy 

15xy = 125 – 35

15xy = 90 

xy = `90/15`

xy = 6

The product of the two numbers x and y is 6.