a = b
ab = b^2
ab - a^2 = b^2 - a^2
a(b - a) = (b - a)(b + a)
a = b + a
a = b; a = a + a
a = 2a
1 = 2?
What happened?
Solution: Look at Steps 4 and 5 in my justification above:
a(b - a) = (b - a)(b + a)
a = b + a
If a = b, then b - a = 0, so the real justification would be:
a(0) = (0)(b + a)
0 = 0
This means I divided by 0 in my justification, which is impossible according to the laws of mathematics.
Hope you enjoyed!
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