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2023 WSMO Accuracy Round Problems/Problem 8

Revision as of 15:36, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>f(x)=x^3-3x^2+4x+5</math> have complex roots <math>a,b,c</math>. Then, the value of <math>\frac{1}{a^2+b^2}+\frac{1}{a^2+c^2}+\frac{1}{b^2+c^2}</math> i...")
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Problem

Let $f(x)=x^3-3x^2+4x+5$ have complex roots $a,b,c$. Then, the value of $\frac{1}{a^2+b^2}+\frac{1}{a^2+c^2}+\frac{1}{b^2+c^2}$ is $\frac{m}{n},$ for relatively prime positive integers $m$ and $n.$ Find $m+n$

Solution

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