Given a≠±b and (a^2−b^2)/(a+b)=12, find a−b.
2 answers:
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Answer:
See explanation
Step-by-step explanation:
Ms. Johnson space has 48 carpet squares.
Mr. Wei space has 36 carpet squares.
Factorize these two numbers:
All common factors are 1, 2, 3, 4, 6, 12
<u>All possibilities:</u>
1. If Ms. Johnson space width and Mr. Wei space width is 1 carpet, then Ms. Johnson space length is 48 carpets and Mr. Wei space length is 36 carpets.
2. If Ms. Johnson space width and Mr. Wei space width is 2 carpets, then Ms. Johnson space length is 24 carpets and Mr. Wei space length is 18 carpets.
3. If Ms. Johnson space width and Mr. Wei space width is 3 carpets, then Ms. Johnson space length is 16 carpets and Mr. Wei space length is 12 carpets.
4. If Ms. Johnson space width and Mr. Wei space width is 4 carpets, then Ms. Johnson space length is 12 carpets and Mr. Wei space length is 9 carpets.
5. If Ms. Johnson space width and Mr. Wei space width is 6 carpets, then Ms. Johnson space length is 8 carpets and Mr. Wei space length is 6 carpets.
6. If Ms. Johnson space width and Mr. Wei space width is 12 carpets, then Ms. Johnson space length is 4 carpets and Mr. Wei space length is 3 carpets.
We can expand the logarithm of a product as a sum of logarithms:
Then using the change of base formula, we can derive the relationship
This immediately tells us that
Notice that none of can be equal to 1. This is because
for any choice of . This means we can safely do the following without worrying about division by 0.
so that
Similarly,
so that
So we end up with
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Another way to do this:
Then
So we have