Solving $(m,n)$ for $m^2-2mn+14n^2=217$

  • MHB
  • Thread starter Albert1
  • Start date
In summary, the equation that needs to be solved for $(m,n)$ is $(m^2-2mn+14n^2=217)$. The variables in the equation are $m$ and $n$, and the method for solving this type of equation is factoring or using the quadratic formula. This equation can have multiple solutions for $(m,n)$, and solving it can help in understanding patterns and relationships between variables, which is important in scientific research in fields such as physics, chemistry, and engineering.
  • #1
Albert1
1,221
0
$m^2-2mn+14n^2=217$
$m,n\in N$
find solution(s) of $(m,n)$
 
Mathematics news on Phys.org
  • #2
Albert said:
$m^2-2mn+14n^2=217$
$m,n\in N$
find solution(s) of $(m,n)$
we have

$(m-n)^2 + 13n^2 = 217$
so $13n^2 < 127$ or $n^2 < 17 ( 13 * 17 = 221)$
trying n = 1,2,3,4,5 we get
n = 3 and m-n = 10 so m = 13 , n =3 is the solution and no other
 
Last edited:
  • #3
kaliprasad said:
we have

$(m-n)^2 + 13n^3 = 217$
so $13n^2 < 127$ or $n^2 < 17 ( 13 * 17 = 221)$
trying n = 1,2,3,4,5 we get
n = 3 and m-n = 10 so m = 13 , n =3 is the solution and no other
sorry! have some others
 
  • #4
Albert said:
sorry! have some others

Yes I missed one more n=4, n-m = 3 giving m = 7, n= 4
 
  • #5
kaliprasad said:
Yes I missed one more n=4, n-m = 3 giving m = 7, n= 4
still one missing
 
  • #6
Albert said:
still one missing

I should have taken |m-n| =3 giving m = 1 and n = 4
 

FAQ: Solving $(m,n)$ for $m^2-2mn+14n^2=217$

What is the equation that needs to be solved for $(m,n)$?

The equation that needs to be solved is $(m^2-2mn+14n^2=217)$.

What are the variables in the equation?

The variables in the equation are $m$ and $n$.

What is the method for solving this type of equation?

The method for solving this type of equation is factoring or using the quadratic formula.

Can this equation have multiple solutions?

Yes, this equation can have multiple solutions for $(m,n)$.

What is the importance of solving this equation in terms of scientific research?

Solving this equation can help in understanding patterns and relationships between variables, which can be useful in various scientific fields such as physics, chemistry, and engineering.

Similar threads

I Finding N / log(2) and M / log(3) very close together
Replies
9
Views
1K
MHB Sum Infinity Express: Rational Number Solution
Replies
4
Views
2K
MHB Is Fermat's Last Theorem Solvable for n=4 Using Pythagorean Triples?
Replies
4
Views
2K
MHB Solving the Equation cos (x)=-0.8
Replies
4
Views
4K
MHB What is the remainder when m+n is divided by 1000 in a trigonometric challenge?
Replies
2
Views
1K
MHB Find Perfect Square $m,n \in N$ with $m^2-4n$ & $n^2-4m$
Replies
5
Views
1K
MHB Find all functions satisfying f(mn)=f(m)f(n), and m+n|f(m)+f(n)
Replies
5
Views
1K
MHB Show that 1^m+2^m+....+(n-2)^m+(n-1)^m is divisible by n
Replies
6
Views
2K
MHB Solve √(x^2+3x+7)-√(x^2-3x+9)+2=0
Replies
5
Views
2K
MHB For which n is the term an integer & Calculate the equivalence
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top