Question: The reciprocal of x’s non-integer decimal part equals x + 1, and x > 0.

Quantity A: x

Quantity B:sqrt(2)

Answer: C

However, to prove the answer, the book assumes that x = sqrt(2), and reaches the conclusion from there that A = B. But how can we know that this does not work for another x != 2? In other words, that D is the answer?

Many thanks!