Question 142
a) Find all real numbers $x$ such that
$$
x^2 + \frac{1}{x^2 + 2x} = 1
$$
b) Find all pairs of positive real numbers $x$ and $y$ such that
$$
x^2 + y^2 + \frac{1}{x^2 + 2x} + \frac{1}{y^2 + 2y} = 2
$$
$$
x^2 + \frac{1}{x^2 + 2x} = 1
$$
b) Find all pairs of positive real numbers $x$ and $y$ such that
$$
x^2 + y^2 + \frac{1}{x^2 + 2x} + \frac{1}{y^2 + 2y} = 2
$$