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2022 SSMO Relay Round 2 Problems/Problem 2

Revision as of 12:10, 14 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>T=</math> TNYWR. Suppose that the monic quadratic <math>f(x)</math> is tangent to the function <math>g(x)=|x+2|-T</math> at two points, when graphed on t...")
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Problem

Let $T=$ TNYWR. Suppose that the monic quadratic $f(x)$ is tangent to the function $g(x)=|x+2|-T$ at two points, when graphed on the coordinate plane. Then $|f(1)|$ can be expressed as $\frac mn$, where $m$ and $n$ are relatively prime positive integers. Find $10m+n$.

Solution

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