Problem 22 · 2018 Math Kangaroo
Stretch
Algebra & Patterns
substitution
\(m\) and \(n\) are the solutions of the equation \(x^2 - x - 2018 = 0\). What is the value of the expression \(n^2 + m\)?
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Answer: D — 2019
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Hint 1 of 2
Use the relations between the roots and the equation they satisfy.
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Hint 2 of 2
Replace n² using the original equation.
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Approach: Vieta plus substituting the equation a root satisfies
- From x²−x−2018 = 0, the roots satisfy m+n = 1.
- Since n is a root, n² = n + 2018.
- Then n² + m = (n + 2018) + m = (m+n) + 2018 = 1 + 2018 = 2019.
- Answer: 2019.
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