Ali W.

asked • 01/29/18

I need to find the value of m and n

m2 - n2 = 21

2 Answers By Expert Tutors

By:

Inactive Tutor answered • 01/29/18

Tutor
New to Wyzant

See tutors like this
See tutors like this
There are multiple solutions. But which one to chose?! This is a question to Student;
52-22=21
or
112-102=21
Upvote • 0 Downvote
More
Report

Ali W.

But how did you get to the answer I just wanna know the process 
Report

01/29/18

Inactive Tutor

Is this question for me or for David?
Report

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 
Report

01/29/18

Inactive Tutor

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. 
Report

01/29/18

David W. answered • 01/29/18

Tutor
4.9 (108)

I'll help you understand math!
About this tutor ›
About this tutor ›
(m - n)(m + n) = 21
 
 I'll give you a hint. They are consecutive.
Upvote • 0 Downvote
More
Report

Ali W.

But how did you get to the answer I just wanna know the process
 
Report

01/29/18

David W.

tutor
Actually, as mentioned, there is more than one value for each. What exactly are your instructions?
Report

01/29/18

Inactive Tutor

Right. Question needs certain specification(s). 
Report

01/29/18

David W.

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

01/29/18

Ali W.

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

01/29/18

David W.

tutor
Does it say "solve for m" and "solve for n"? Those do not come up with integers.
Report

01/29/18

Inactive Tutor

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. 
 
Report

01/29/18

Inactive Tutor

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. 
Report

01/29/18

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.