I will let x,y,z be the three roots, and 2024 is generalized to k.
First I gave the big expression a common denominator and did some tedious algebra:
[3k^3 - (x+y+z)*k^2 - (xy+xz+yz)*k + 3xyz] / [k^3 - (x+y+z)*k^2 + (xy+xz+yz)*k - xyz]
Then from the given cubic equation xyz=1, xy+yz+xz=-1, and x+y+z=0. Substitute these into the expression:
[3k^3 - 0*k^2 - -1*k + 3*1] / [k^3 - 0*k^2 + -1*k - 1]
Then we get a simplified form of [3k^3+k+3]/[k^3-k-1], then at k=2024 we have a value of [3*2024^3+2024+3]/[2024^3-2024-1] = 24874411499/8291467799
Solution
