Question 1
(a) Determine a nonzero polynomial in $x$ of least degree with integer coefficients having $\sqrt2+\sqrt[3]3$ as a root.
(b) Solve
$$1+\sqrt{1+x^2}\left(\sqrt{(1+x)^3}-\sqrt{(1-x)^3}\right)=2+\sqrt{1-x^2}.$$
(b) Solve
$$1+\sqrt{1+x^2}\left(\sqrt{(1+x)^3}-\sqrt{(1-x)^3}\right)=2+\sqrt{1-x^2}.$$