Question 99
The functions $f(x) = 2x^2 + 2x - 4$ and $g(x) = x^2 - x + 2$ are given. Find all real values of $x$ such that:
a) $\frac{f(x)}{g(x)}$ is a positive integer;
b) the inequality $\sqrt{f(x)} + \sqrt{g(x)} \ge \sqrt{2}$ holds.
a) $\frac{f(x)}{g(x)}$ is a positive integer;
b) the inequality $\sqrt{f(x)} + \sqrt{g(x)} \ge \sqrt{2}$ holds.