SOLUTION: Give a counterexample to show that (x+y)2 = x2 + y2 is false.

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Question 737616: Give a counterexample to show that (x+y)2 = x2 + y2 is false.
Found 2 solutions by richwmiller, MathLover1:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
let x=1 y=2
(1+2)^2=1^2+2^2
3^2=1+4
9=5
not true

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

To find a counter example to "%28x%2B+y%29%5E2 is NOT x%5E2%2B+y%5E2", you must use x and y so that %28x%2By%29%5E2=+x%5E2%2B+y%5E2.
Presumably you know that %28x%2B+y%29%5E2=+x%5E2%2B+2xy%2B+y%5E2. That means you must find x and y so that x%5E2%2B+2xy%2B+y%5E2=+x%5E2%2B+y%5E2.
cross%28x%5E2%29%2B+2xy%2B+cross%28y%5E2%29=+cross%28x%5E2%29%2B+cross%28y%5E2%29...notice that the squares on both sides cancel
What does that leave you with?
2xy=+0...this is true only if only x=0 or y=0, or both x=0 and y=0
so, it proves that %28x%2B+y%29%5E2%3C%3Ex%5E2%2B+y%5E2