Home Competitions AHSME 1980 Problem 29
How many ordered triples (x,y,z) of integers satisfy the system of equations below?
x 2 − 3 x y + 2 y 2 − z 2 = 31 − x 2 + 6 y z + 2 z 2 = 44 x 2 + x y + 8 z 2 = 100 \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} x 2 − 3 x y + 2 y 2 − z 2 = 31 − x 2 + 6 y z + 2 z 2 = 44 x 2 + x y + 8 z 2 = 100 (A) 0 (B) 1 (C) 2 (D) a finite number greater than 2 (E) infinitely many \text{(A)} \ 0 \text{(B)} \ 1 \text{(C)} \ 2 \\ \text{(D)}\ \text{a finite number greater than 2} \\ \text{(E)}\ \text{infinitely many} (A) 0 (B) 1 (C) 2 (D) a finite number greater than 2 (E) infinitely many
Dataset text NuminaMath-1.5 . Quoted with source.
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