Find a monic quartic polynomial with rational coefficients whose roots include x = 1 - sqrt(2) and x = 2 + sqrt(7).
If 1 - sqrt 2 and 2 + sqrt 7 are roots, then so are the conjugates 1 + sqrt 2 and 2 - sqrt 7
We just need to simplify this
( x - (1 - sqrt 2) ) ( x - ( 1 + sqrt 2)) ( x - (2 + sqrt 7)) ( x - ( 2 - sqrt 7)) =
x^4 - 6 x^3 + 4 x^2 + 10 x + 3