VMO 1984 Problem 1

(1) Find a polynomial with integral coefficients which has the real number $2^{1/2}$ + $3^{1/3}$ as a root and the smallest possible degree. (2) Find all real solutions to 1 + √(1 + $x^2$) (√(1 + x)$^3$ - √(1 - x)$^3$ ) = 2 + √(1 - $x^2$).