17.19 USE problems

Problem: The quadratic equation \( x^{2}+p x+q=0 \) has two different roots \( x_{1} \) and \( x_{2} \). Find \( p \) and \( q \), if the numbers of \( x_{1}+1 \) и \( x_{2}+1 \) are the roots of the equation \( x^{2}-p^{2} x+p q=0 \).