SOLUTION: if the difference of any two numbers is 6 and their product is 18. what is the sum of their squares?

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Question 500309: if the difference of any two numbers is 6 and their product is 18. what is the sum of their squares?
Answer by solver91311(24713) About Me  (Show Source):
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Let represent one of the numbers. Let represent the other number. Then:



and



Solve the first equation for



Substitute into the second equation:





Solve the quadratic either by completing the square or using the quadratic formula.



Then, since





We want the sum of the squares, so calculate:



Then calculate:



Verification that , the correctness of the solutions to the quadratic equation, and that the results of the calculation of is the same for both the positive and negative roots is left as an exercise for the student.

John

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