91Ó°ÊÓ

The expression is,

$\sqrt{r}+6=\sqrt{r+8}$.

$\sqrt{r}+6=\sqrt{r+8}$

Squaring both sides,

role="math" localid="1647943273549" $$\begin{gathered} ⇒{(\sqrt{r}+6)}^2={\left(\sqrt{r+8}\right)}^2 \\ ⇒r+36+12\sqrt{r}=r+8 \end{gathered}$$

Simplifying the equation,

$$\begin{gathered} ⇒12\sqrt{r}=r+8-r-36 \\ ⇒12\sqrt{r}=-24 \end{gathered}$$

Dividing both sides by $12$,

$⇒\sqrt{r}=-2$

Squaring both sides,

role="math" localid="1647943414805" $$\begin{gathered} ⇒{\left(\sqrt{r}\right)}^2={(-2)}^2 \\ ⇒r=4 \end{gathered}$$

Inputting $r=4$,

$\sqrt{r}+6=\sqrt{4}+6$

$$\begin{gathered} =2+6 \\ =8 \end{gathered}$$

$\sqrt{r+8}=\sqrt{4+8}$

$=\sqrt{12}$

The expression is,

$\sqrt{s-3}+2=\sqrt{s+4}$.

$\sqrt{s-3}+2=\sqrt{s+4}$

Squaring both sides,

role="math" localid="1647944065264" $$\begin{gathered} ⇒{(\sqrt{s-3}+2)}^2={\left(\sqrt{s+4}\right)}^2 \\ ⇒s-3+4+4\sqrt{s-3}=s+4 \\ ⇒s+1+4\sqrt{s-3}=s+4 \end{gathered}$$

Simplifying the equations,

$$\begin{gathered} ⇒4\sqrt{s-3}=s+4-s-1 \\ ⇒4\sqrt{s-3}=3 \end{gathered}$$

Squaring both sides,

role="math" localid="1647944181620" $$\begin{gathered} ⇒{\left(4\sqrt{s-3}\right)}^2={\left(3\right)}^2 \\ ⇒16(s-3)=9 \end{gathered}$$

Simplifying the equations,

$$\begin{gathered} ⇒16s-48=9 \\ ⇒16s=9+48 \\ ⇒16s=⇒57 \\ ⇒s=\frac{57}{16} \end{gathered}$$

Inputting $s=\frac{57}{16}$,

$\sqrt{s-3}+2=\sqrt{\frac{57}{16}-3}+2$

$$\begin{gathered} =\sqrt{\frac{9}{16}+2} \\ =\frac{3}{4}+2 \\ =\frac{11}{4} \end{gathered}$$

$\sqrt{s+4}=\sqrt{\frac{57}{16}+4}$

$$\begin{gathered} =\sqrt{\frac{121}{16}} \\ =\frac{11}{4} \end{gathered}$$

This solution is true.