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The sum of 3 real numbers is known to be zero. If the sum of their cubes is -1, what is their product equal to?

 Apr 25, 2021
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a+b+c=0

a^3+b^3+c^3=-1

 

a+b=-c

 

a^3+b^3 - (a+b)^3  = -1

(a+b)^3 = a^3 +b^3 +3abb +3aab

 

Cancel cubes

3aab + 3abb = -1

3ab(a+b)=-1

3ab(-c) =-1

3abc = 1

abc = 1/3

 Apr 25, 2021

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