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

Question

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

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4 months 2021-07-18T23:38:29+00:00 2 Answers 0 views 0

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# ItzYourQueen01

• 152 is the sum of their cubes

## Given:

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

## Tofind:

• 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