Positive square rationals equidistant to 1

Question

Can there be two square rational numbers that are equidistant to $1$ i.e. there is a rational number $a \in [0,1]$ such that both $1-a$ and $1+a$ are square rationals?

Answer 1

Note that two numbers that sum to 2 are equidistant to 1. Now take your favorite Pythagorean triple

$$x^2 + y^2 = z^2$$

and see that

$$\frac{(x - y)^2}{z^2} + \frac{(x + y)^2}{z^2} = 2$$

Answer 2

Hint : $$1+49 = 2 \times 25$$