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everything is fine, but once the factorization has been obtained, Vieta's theorem can be applied. You can also simply factorize the free term so that they differ by one 1111122222=11111*2*3*16667=33333*33334. And also apply Vieta’s theorem.
If you add 3*3+3,you get 12,in the same way if you multiply 33 with 33 and add 33 you get 1122,in the same way if you need to get 1111122222(that is,five 1's and five 2's)your answer must be 33333(five 3's)
I solved by realzing it is X(X+1) which is two consecute numbers. The square root of 1111122222 will be between them andthe answer is the lower of the two numbers.