75. (9th grade) Solve the equation $\sqrt[4]{8-x}+\sqrt[4]{89+x}=5$.
75. We introduce the notations: $8-x=a^{4}, 89+x=b^{4}$.

Solving the equation reduces to solving two systems of equations:

$$
\text { a) }\left\{\begin{array}{l}
a+b=5 \\
a b=44
\end{array}\right.
$$

There are no real roots. b) $\{a+b=5$

$a b=6$

$a=2, \quad b=3$ or $b=2, \quad a=3$

Answer: $x_{1}=-8, \quad x_{2}=-73$.