Verified answer

[tex] \frac{p + 4}{p - 2} = \frac{2p - 7}{p - 4} \\ (2p - 7)(p - 2) = (p + 4)(p - 4) \\ 2 {p}^{2} - 4p - 7p + 14 = {p}^{2} - 16 \\ 2 {p}^{2} - 11p + 14 - {p}^{2} + 16 = 0 \\ {p}^{2} - 11p + 30 = 0[/tex]

По теореме Виета:

[tex]{x}^{2} + bx + c = 0 \\ x _{1} + x_{2} = - b \\ x _{1} x_{2} = c[/tex]

[tex]p_{1} + p_{2} = 11\\ p _{1} p_{2} =30 \\ p_{1} = 5\\ p_{2} = 6[/tex]