Chapter 10 - Radical Expressions and Equations - 10-4 Solving Radical Equations - Practice and Problem-Solving Exercises - Page 624: 45

no solution

$\sqrt {7p+5} = \sqrt{p-3}$ $(\sqrt {7p+5})^2 =(\sqrt{p-3})^2$ $7p+5 = p-3$ $7p+5-p+3 = p-3-p+3$ $6p+8 = 0$ $(6p+8)/2 = 0/2$ $3p+4 = 0$ $3p+4-4 = 0-4$ $3p= -4$ $3p/3 = -4/3$ $p = -4/3$ $\sqrt {7p+5} = \sqrt{p-3}$ $\sqrt {7*-4/3+5} = \sqrt{-4/3-3}$ $\sqrt {-28/3+5} = \sqrt{-4/3+-3}$ $\sqrt {-43/3} \ne \sqrt {-13/3}$ (no solution)