Chapter 1 - Equations and Inequalities - 1.6 Other Types of Equations and Applications - 1.6 Exercises - Page 149: 114

$\{ 4\}$

Step 1. Let $u=\sqrt x$, we have $3u^2-2u-8=0$ Step 2. Factor and solve the equation: $(u-2)(3u+4)=0$, thus $u=-\frac{4}{3}, 2$ Step 3. For $u=2$, we have $\sqrt x=2$, thus $x=4$ Step 4. For $u=-\frac{4}{3}$, we have $\sqrt x=-\frac{4}{3}$, no real solution. Step 5. Check answers in the original equation, only $\{ 4\}$ fits.