Find the error in the following proof that 2 = 1. Consider the equation a = b. Multiply both sides by a to obtain a 2 = ab. Subtract b 2 from both sides to get a 2 - b 2 = ab - b 2. Now factor each side, (a + b) (a - b) = b (a - b), and divide each side by (a - b) to get a + b = b. Finally, let a and b equal 1, which shows that 2 = 1.

Question

Kylie Pennington

Engineering

8 January, 06:27

Find the error in the following proof that 2 = 1. Consider the equation a = b. Multiply both sides by a to obtain a 2 = ab. Subtract b 2 from both sides to get a 2 - b 2 = ab - b 2. Now factor each side, (a + b) (a - b) = b (a - b), and divide each side by (a - b) to get a + b = b. Finally, let a and b equal 1, which shows that 2 = 1.

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Answers (1)

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Tristin · Answer 1

You can't divide by zero

Explanation:

The error appears when you divide each side by (a - b). If a = b, then (a - b) = 0 and you can't divide each side by 0. Moreover, the equation before division, that is, (a + b) (a - b) = b (a - b) is true after replacing (a - b) = 0 because it gives 0 = 0.