SOLUTION: Find a value for k so that 9m squared - kn squared will have the factors 3m + 7n and 3m

SOLUTION: Find a value for k so that 9m squared - kn squared will have the factors 3m + 7n and 3m - 7n

Question 114234: Find a value for k so that 9m squared - kn squared will have the factors 3m + 7n and 3m - 7n
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find a value for k so that 9m squared - kn squared will have the factors 3m + 7n and 3m - 7n
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If they are factors:
9m^2-kn^2 = (3m+7n)(3m-7n)
9m^2-kn^2 = 9m^2-49n^2
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-k = -49
k = 49
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Cheers,
Stan H.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
is the difference of two squares, so you are looking for something that fits the pattern:

, or put another way,

That means that the factorization of is

But, must equal according to the conditions of the problem. Therefore we can set

+++++++++++++++++++++++++++++++++++++++++++++++++++++++
A simpler method just to get to the answer straightaway would be to simply apply FOIL to

, and you can see by inspection that k = 49.

Hope that helps,
John
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