Difference between revisions of "1980 AHSME Problems/Problem 29"

m (Problem)
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How many ordered triples (x,y,z) of integers satisfy the system of equations below?  
 
How many ordered triples (x,y,z) of integers satisfy the system of equations below?  
  
<cmath>\begin{array}{l} x^2-3xy+2yz-z^2=31 \\ -x^2+6yz+2z^2=44 \\ x^2+xy+8z^2=100\\ \end{array} </cmath>
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<cmath>\begin{array}{l} x^2-3xy+2y^2-z^2=31 \\ -x^2+6yz+2z^2=44 \\ x^2+xy+8z^2=100\\ \end{array} </cmath>
  
 
<math>\text{(A)} \ 0 \qquad  
 
<math>\text{(A)} \ 0 \qquad  

Revision as of 17:31, 6 January 2019

Problem

How many ordered triples (x,y,z) of integers satisfy the system of equations below?

\[\begin{array}{l} x^2-3xy+2y^2-z^2=31 \\ -x^2+6yz+2z^2=44 \\ x^2+xy+8z^2=100\\ \end{array}\]

$\text{(A)} \ 0 \qquad  \text{(B)} \ 1 \qquad  \text{(C)} \ 2 \qquad \\ \text{(D)}\ \text{a finite number greater than 2}\qquad\\ \text{(E)}\ \text{infinitely many}$

Solution

$\fbox{}$

See also

1980 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 28
Followed by
Problem 30
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
All AHSME Problems and Solutions

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