ISL 1988 Problem 86

Let $a,b,c$ be integers different from zero. It is known that the equation $a \cdot x^2 + b \cdot y^2 + c \cdot z^2 = 0$ has a solution $(x,y,z)$ in integer numbers different from the solutions $x = y = z = 0.$ Prove that the equation $$a \cdot x^2 + b \cdot y^2 + c \cdot z^2 = 1$$ has a solution in rational numbers.