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National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1976 AMC 12/AHSME
30
30
Part of
1976 AMC 12/AHSME
Problems
(1)
Find all triples (x,y,z)
Source: 1976 AHSME Problem 30
5/19/2014
How many distinct ordered triples
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
satisfy the equations \begin{align*}x+2y+4z&=12 \\ xy+4yz+2xz&=22 \\ xyz&=6~~?\end{align*}
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<span class='latex-bold'>(A) </span>\text{none}\qquad<span class='latex-bold'>(B) </span>1\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>4\qquad <span class='latex-bold'>(E) </span>6
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6
AMC