1976 AHSME Problems/Problem 30
Problem 30
How many distinct ordered triples satisfy the following equations?
Solution
The first equation suggests the substitution from which
We rewrite the given equations in terms of and We clear fractions in these equations: By Vieta's Formulas, note that and are the roots of the equation which factors as It follows that Since the substitution is not symmetric with respect to and we conclude that different ordered triples generate different ordered triples as shown below: So, there are such ordered triples
~MRENTHUSIASM (credit given to AoPS)
See also
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