Ali W.

asked • 01/29/18

I need to find the value of m and n

m2 - n2 = 21

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Bobosharif S. answered • 01/29/18

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There are multiple solutions. But which one to chose?! This is a question to Student;
52-22=21
or
112-102=21
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Ali W.

But how did you get to the answer I just wanna know the process 
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01/29/18

Bobosharif S.

Is this question for me or for David?
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01/29/18

Ali W.

this question is for both and it’s that I don’t need the answer I just need to now how to get to it not using process of elimination 
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01/29/18

Bobosharif S.

Ali from New York, NY. Look, in general, your equation is with two variables, you can "let free" one of them and find another one, for instance, you can m=±√(21+n2). You can vary n within any possible set (domain) and find m. And this way you will obtain many (infinite, in principle) pairs of  (m, n). Therefore, a question arises: where to look for (m, n).
Above explanation is one of the ways how to find m and n. 
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01/29/18

David W. answered • 01/29/18

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(m - n)(m + n) = 21
 
 I'll give you a hint. They are consecutive.
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Ali W.

But how did you get to the answer I just wanna know the process
 
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01/29/18

David W.

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Actually, as mentioned, there is more than one value for each. What exactly are your instructions?
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01/29/18

Bobosharif S.

Right. Question needs certain specification(s). 
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01/29/18

David W.

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I simply played around with different squares of numbers.
 
64 - 9 ≠ 21, for example.
 
Again, I ask what your specific instructions are.
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01/29/18

Ali W.

You must solve it but you can’t play around with potential solutions u need I direct mathematical solution
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01/29/18

David W.

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Does it say "solve for m" and "solve for n"? Those do not come up with integers.
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01/29/18

Bobosharif S.

Say, set of solution should be specified; where are we looking for solution. If m and n are reals, this is one set, integers another (smaller) set, positive integers even more smaller set. In principle, they can be complex numbers as well.
Assuming m and n are integers, from equation you wrote (m-n)(m+n)=21 follows that
m-n=3  
m+n=7
or vice versa.
If we remove that "if" in the RHS of the last equation you can nay any numbers, a and b, such that a*b=21 and solve that system of equations fro m and n. 
 
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01/29/18

Bobosharif S.

My apologies: Typing errors.
If we remove that "if" in the RHS of the last equation you can write any two numbers, a and b, such that a*b=21 and solve that system of equations for m and n. 
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01/29/18

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