Question 177
Let $k$ be such a natural number that it has a quadratic equation
$$
k x^{2}-(1-2 k) x+k-2=0
$$
rational solutions. Prove that $k$ is the product of 2 consecutive integers.
$$
k x^{2}-(1-2 k) x+k-2=0
$$
rational solutions. Prove that $k$ is the product of 2 consecutive integers.