Brain Teasers
5 * 7 = 37
According to basic algebra, (A + B)(A - B) is equal to A^2 - B^2 (A^2 is "A squared"). Substituting 1 for B, we get A^2 - 1^2.
A^2 - 1^2 is the same as A^2 + (-1^2). Since -1 times -1 is one, we end up with A^2 + 1.
If we substitute 6 for A, we get (6+1)(6-1) = 6^2+1, or 37. Since 6+1 is 7 and 6-1 is 5, five times seven is thirty-seven.
What's wrong with this proof?
A^2 - 1^2 is the same as A^2 + (-1^2). Since -1 times -1 is one, we end up with A^2 + 1.
If we substitute 6 for A, we get (6+1)(6-1) = 6^2+1, or 37. Since 6+1 is 7 and 6-1 is 5, five times seven is thirty-seven.
What's wrong with this proof?
Answer
A^2 - 1^2 is NOT the same as A^2 + (-1^2). It is actually A^2 + -(1^2), or the negative of 1 * 1.Hide Answer Show Answer
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Comments
dakarmorad nicely done teaser. It has been too long since I've done an algerbraic problem. Thanks for making it fun to remember.
What the...good job tricking me...
Very, very easy but nice try.
Mar 15, 2006
Isn't (A + B)(A - B) equal to
(A^2) + (BA) - (AB) -(B^2)?
(A^2) + (BA) - (AB) -(B^2)?
Mar 15, 2006
Oops, sorry, I overlooked AB canceling itself out.
That was fairly simple. Raising to a power is a higher order operation than negation.
Too easy!
Testing basic algebra knowledge, Quite easy.
This just made no sense. I think the "what's wrong with this" should come first. Then I won't have condescending thoughts about the author when I see the obvious error.
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