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Use the identity a^3+b^3=(a+b)^3 - 3ab(a+b) to determine the product of the two numbers if the sum of the cubes of the two numbers is 152 and the sum of the two numbers is 8.

 Feb 19, 2020
 #1
avatar+109740 
+1

We have that

 

a^3 + b^3  =  152      and       a + b   = 8

 

So  we have that

 

152  =  (a + b)^3 - 3ab ( a + b)

 

152  =   (8)^3  - 3ab (8)

 

152  =  512  - 24ab     rearrange as

 

24ab  = 512  - 152

 

24ab  = 360     divide both sides by  24

 

ab  = 15   →   (the product of the two numbers )

 

BTW.....the numbers are 3 and 5  ....

 

cool cool cool

 Feb 19, 2020
 #2
avatar+11731 
+1

Use the identity a^3+b^3=(a+b)^3 - 3ab(a+b) to determine the product of the two numbers if the sum of the cubes of the two numbers is 152 and the sum of the two numbers is 8.

laugh

 Feb 19, 2020

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