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Question 944520: The sum ot two numbers is 6 and their product is 7. What is the sum of their cubes?
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! x+y = 6
xy = 7
Using sum of cubes,
x^3 + y^3 = (x+y)(x^2 - xy + y^2) = 6(x^2 + y^2 - 7)
To find x^2 + y^2, we have (x+y)^2 = 36 = x^2 + y^2 + 2xy = x^2 + y^2 + 2*7, so x^2 + y^2 = 36 - 14 = 22.
Then x^3 + y^3 = 6(22 - 7) = 90.
An alternate solution is to solve the quadratic x^2 - 6x + 7 for both its roots, obtaining 3 + sqrt(2) and 3 - sqrt(2), cubing and summing also gives 90.
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