1955 AHSME Problems/Problem 30
Each of the equations has:
Since the question asks us about the unifying characteristic of all three equations' roots, we have to first determine them.
can be rewritten as , which gives the following roots and .
can be expanded to , which in turn leads to . The roots here are and .
, when squared, also turns into a quadratic equation: . Binomial factoring gives us the roots and .
We can clearly see that, between all of the equations, there is .
Note: There are probably extraneous solutions somewhere, but that does not affect the solution.
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