Smallest Inequality Bound

Algebra Level 5

What is the smallest integer NN such that (x43x26x+13x4x2+1)4<N \left( \sqrt{ x^4 - 3x^2 - 6x +13} - \sqrt{x^4 - x^2 +1 } \right) ^4 < N, as x x ranges over all real values?

Note: There is a strict inequality in the challenge.

Details and assumptions

If you think that the expression can take values over 999, input your answer as 999.


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