1977 USAMO Problems/Problem 3
If and are two of the roots of , prove that is a root of .
This problem needs a solution. If you have a solution for it, please help us out by. a,b,c,d are roots of equation then by vietas relation let us suppose are roots of .
then sum of roots sum taken two at a time similarly we prove for the roots taken three four five and six at a time to prove are roots of second equation
Given the roots of the equation .
Then and .
Remains or .
Let and , so (1).
Second, is a root, and is a root, .
Multiplying: or .
In (1): .
Conclusion: is a root of .
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