Problem:
If and are positive real numbers and each of the equations and has real roots, then the smallest possible value of is
Answer Choices:
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Solution:
That the roots of are both real implies that the discriminant is nonnegative, that is, . Likewise, that has real roots implies or . Thus . Since , one obtains and so and . Conversely, does result in real roots for both (identical) equations. Thus the minimum value of is .