Question 142
Let $x = -\sqrt{2} + \sqrt{3} + \sqrt{5}$, $y = \sqrt{2} - \sqrt{3} + \sqrt{5}$, and $z = \sqrt{2} + \sqrt{3} - \sqrt{5}$. What is the value of the expression below?
$$
\frac{x^{4}}{(x-y)(x-z)} + \frac{y^{4}}{(y-z)(y-x)} + \frac{z^{4}}{(z-x)(z-y)}
$$
$$
\frac{x^{4}}{(x-y)(x-z)} + \frac{y^{4}}{(y-z)(y-x)} + \frac{z^{4}}{(z-x)(z-y)}
$$