SOLUTION: 1) (x-y-1)^2 + (x+y-7)^2=0 find x+y

Question 724427: 1) (x-y-1)^2 + (x+y-7)^2=0 find x+y
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
This looks like it might be an SAT problem. To solve it you have to employ some "outside the box" thinking:

The equation, at its very essence, says that the sum of two numbers is equal to zero. Now ask yourself: "How do numbers add up to zero?" Maybe you've never thought of this question before. But it should be difficult to understand that two numbers add up to zero in exactly two ways:
- Both numbers are zeros; or
- The numbers are opposites of each other, one positive and one negative
The two numbers we are adding are the result of squaring something. What kind of results to you get when you square something? Answer: You get zero or some positive number. Squaring a real number never results in a negative! So if we're adding the results of squaring two numbers we cannot have the "one positive and one negative" that adds up to zero.

So the only way this equation can be true is if both squares are zeros! And to get a zero result from squaring you must be squaring a zero. So:
x-y-1 = 0
and
x+y-7 = 0

We could find both x and y by solving this system. Then we could find x+y by adding them. But it's quicker if you just add 7 to each side of the second equation:
x+y = 7
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