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Difference between revisions of "2022 SSMO Relay Round 2 Problems/Problem 2"

(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==
 
==Problem==
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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 the coordinate plane. Then <math>|f(1)|</math> can be expressed as <math>\frac mn</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>10m+n</math>.
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Let <math>T=TNYWR</math>. 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 the coordinate plane. Then <math>|f(1)|</math> can be expressed as <math>\frac mn</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>10m+n</math>.
  
 
==Solution==
 
==Solution==

Latest revision as of 19:23, 2 May 2025

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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