## 1 = 2Math brain teasers require computations to solve.
Bob and Sue were having a discussion one day about 1 and 2. Sue reckoned she had seen a way that you could make 1 = 2 but Bob who wasn't called 'logical Bob' for nothing was obviously adamant that this just wasn't possible. Sue said "Ok smarty pants here's the equation to prove you wrong"...
Assumptions: There are two numbers, a and b, and they are equal. Proof: a = b Multiply the equation by b ab = b^2 Subtract a^2 from the equation ab - a^2 = b^2 - a^2 Factor difference of squares ab - a^2 = (b - a)(b + a) Factor a on the left-hand side a(b - a) = (b - a)(b + a) Divide by common factor a = (b + a) Substitute a for b a = (a + a) Simplify a = 2a Divide by common factor 1 = 2 Question: Bob didn't take long and found the line where there is a crucial mistake in the working though was understanding of Sue's issue as it is well hidden... can you see it? ## AnswerGoing from a(b - a) = (b - a)(b + a) to a = (b + a) is not allowed, because the equation is divided by (b - a), which is equal to 0, given that a = b.Hide ## What Next?
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