SOLUTION: I am thinking of two numbers. The sum of the number is 3; the sum of their squares is 29. What are the numbers?

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Question 657487: I am thinking of two numbers. The sum of the number is 3; the sum of their squares is 29. What are the numbers?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call the two numbers x and y.
The problem tells us that x%2By=3 and x%5E2%2By%5E2=29.

x%2By=3 --> %28x%2By%29%5E2=3%5E2 --> x%5E2%2By%5E2%2B2xy=9
Subtracting x%5E2%2By%5E2=29 from x%5E2%2By%5E2%2B2xy=9, we get.
x%5E2%2By%5E2%2B2xy-x%5E2-y%5E2=9-29 --> 2xy=-20 --> xy=-10

We can find number that satisfy xy=-10 and x%2By=3.
We see that highlight%285%29 and highlight%28-2%29 work.

We could also set up and solve a quadratic equation
xy=-10 --> y=-10%2Fx (dividing both sides by x)
and substituting into x%2By=3, we get
x-10%2Fx=3 --> x%5E2-10=3x (multiplying both sides times x)
Then x%5E2-10=3x --> x%5E2-3x-10=0 (subtracting 3x from both sides).
Of course, we find the same solutions.
We find x=5, which leads to y=-2
and we find x=-2, which leads to y=5.
Either way, the numbers are highlight%285%29 and highlight%28-2%29.
It does not matter which number we call x.