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Question 1033513: The sum of two numbers is 1 and the sum of their squares is 13. What is the sum of their cubes?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The sum of two numbers is 1
a + b = 1
a = (-b+1)
and the sum of their squares is 13.
a^2 + b^2 = 13
Replace a with (-b+1)
(-b+1)^2 + b^2 = 13
FOIL (-b+1)(-b+1)
b^2 - 2b + 1 + b^2 = 13
a quadratic equation
2b^2 - 2b - 12 = 0
simplify, divide by 2
b^2 - b - 6 = 0
Factors to
(b-3)(b+2) = 0
Two solution pairs, essentially the same
b = 3, then a = -2
and
b = -2, then a = 3
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What is the sum of their cubes?
3^3 + -2^3 = 27 - 8 = 19
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Check in the 2nd equation
3^2 + -2^2 = 9 + 4 = 13
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