Contradiction: Prove 2+2 = 5 [duplicate]

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While browsing I came across a weird proof which says 2 + 2 = 5. The proof is like this:

After going through this for almost 30 minutes, I was not able to figure out the mistake in this. What is wrong in this?

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2 Answers

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$$ 4 - \frac92 \ne \sqrt{\left(4 - \frac92\right)^2} \text{ since } 4 - \frac92 < 0. $$

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$$\sqrt{(4-\frac 9 2)^2}=|4-\frac 92|=\frac12 \neq -\frac12 $$

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