Consider two arbitrary numbers a and b. Let
Rearrange this in two ways to get two new valid equations:
a = -b + 2c
Multiply the corresponding sides of the two equations:
Now add c2 to each side and simplify:
(a-c)2 = (b-c)2
Finally, take the root of both sides:
a = b
Consequently, two arbitrarily chosen numbers a and b must be equal!
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