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Omni-MATH / Let f(x)=x³+3x−1 have roots a,b,c. Given that (1)/(a³+b³)+(1)/(b³+c³)+(1)/(c³+a³) can be written as (m)/(n), where m,n are positive integers and gcd(m,n)=1, find 100m+n. · Discussion

Discussing Let f(x)=x³+3x−1 have roots a,b,c. Given that (1)/(a³+b³)+(1)/(b³+c³)+(1)/(c³+a³) can be written as (m)/(n), where m,n are positive integers and gcd(m,n)=1, find 100m+n. · Omni-MATH

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