1. Suppose that a = b
Multiply by a.
Then:
2. a² = ab
Subtract b². then:
3. a² - b² = ab - b²
But a² - b² is the same as (a + b) (a – b).
and ab - b² is the same as b (a – b)
So:
4. (a + b) (a – b) = b (a – b)
Divide by (a – b)
Then:
5. a + b = b.
But a = b.
Therefore:
a + b = 2b
So:
6. 2b = b
Divide by b.
Then:
7. 2 = 1.
But we know this can't be right. What is wrong with this?
Multiply by a.
Then:
2. a² = ab
Subtract b². then:
3. a² - b² = ab - b²
But a² - b² is the same as (a + b) (a – b).
and ab - b² is the same as b (a – b)
So:
4. (a + b) (a – b) = b (a – b)
Divide by (a – b)
Then:
5. a + b = b.
But a = b.
Therefore:
a + b = 2b
So:
6. 2b = b
Divide by b.
Then:
7. 2 = 1.
But we know this can't be right. What is wrong with this?
2 comments:
Hi!
This is false. Yes.
The person who said this was wrong because he doesn't stop to think a bit... you can't divide by zero (Or this says Cariri jajaja).
The mistake is in the fouth step:
4. (a + b) (a – b) = b (a – b)
Divide by (a – b)
If a = b, a - b is zero. But there're to stop a moment to found the mistake, apparently all is correct.
Very good, Alex! You got it right! I'll tell Cariri to give you an extra point...
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