Question

If the sum and the product of two numbers are 8 and 15 respectively, find the sum of
their cubes.​

Answer 1

Answer :

• 152 is the sum of their cubes

Given :

• The sum and the product of two numbers are 8 and 15

To find :

• The sum of their cubes

Solution :

• Let the two number be x and y

》Sum of numbers = 8

》x + y = 8

》x = 8 - y

》Product of numbers are 15

》xy = 15

》y = 15/x

Now ,

》8 - x = 15/x

》x(8 - x) = 15

》-(x)² + 8x = 15

》-(x)² - 8x - 15 = 0

》((-x)² - 8x - 15)) = 0

》-(x - 3) (x - 5) = 0

》x - 3 and x - 5

》x = 3 and x = 5

• If x = 3 then y = 5
• If x = 5 then x = 3

Now , we need to find the sum of their cubes :

》(x)³ + (y)³

》(3)³ + (5)³

》27 + 75

》152

Hence,152 is the sum of their cubes

Verification :

》x + y = 8

》3 + 5 = 8

》8 = 8

Hence Verified