Chapter 8.1, Problem 47STP

To determine

To find: The solution of the given equation or inequality.

Answer to Problem 47STP

The solution of the given equation or inequality is $d>-\frac{3}{4}$ .

Explanation of Solution

Given information:

The given inequality is,

  $\sqrt{d+3}+\sqrt{d+7}>4$

The given inequality is solved as,

  $\begin{array}{l}\sqrt{d+3}+\sqrt{d+7}>4\\ {\left(\sqrt{d+3}+\sqrt{d+7}\right)}^2>{\left(4\right)}^2\\ {\left(\sqrt{d+3}\right)}^2+{\left(\sqrt{d+7}\right)}^2+2\left(\sqrt{d+3}\right)\left(\sqrt{d+7}\right)>16\\ d+3+d+7+2\sqrt{d^2+10d+21}>16\end{array}$

Simplify further,

  $\begin{array}{l}\sqrt{d^2+10d+21}>3-d\\ {\left(\sqrt{d^2+10d+21}\right)}^2>{\left(3-d\right)}^2\\ d^2+10d+21>9+d^2-6d\\ d>-\frac{3}{4}\end{array}$

Thus, the solution of the given equation or inequality is $d>-\frac{3}{4}$ .