Respuesta :
The given equation is
[tex]\frac{24}{\sqrt{x-16}}-\sqrt{x}=\sqrt{x-16}[/tex]First, we multiply both sides to the square root of (x-16), as follows
[tex]\begin{gathered} (\frac{24}{\sqrt{x-16}}-\sqrt{x})\cdot\sqrt{x-16}=\sqrt{x-16}\cdot\sqrt{x-16} \\ \frac{24\cdot\sqrt{x-16}}{\sqrt{x-16}}-\sqrt{x}\cdot\sqrt{x-16}=x-16 \\ 24-\sqrt{x(x-16)}=x-16 \end{gathered}[/tex]Now that we have just one root, we can subtract 24 on both sides
[tex]\begin{gathered} 24-\sqrt{x(x-16)}-24=x-16-24 \\ -\sqrt{x(x-16)}=x-40 \end{gathered}[/tex]Then, we elevate both sides to the square power
[tex]\begin{gathered} (-\sqrt{x(x-16)})^2=(x-40)^2 \\ x(x-16)=x^2-2(40)x+40^2 \\ x(x-16)=x^2-80x+1600 \end{gathered}[/tex]To solve (x-40)2, we used the formula
[tex](a-b)^2=a^2-2ab+b^2[/tex]Now, we solve for x
[tex]\begin{gathered} x^2-16x=x^2-80x+1600 \\ x^2-x^2-16x+80x=1600 \\ 64x=1600 \end{gathered}[/tex]At last, we divide the equation by 64
[tex]\begin{gathered} \frac{64x}{64}=\frac{1600}{64} \\ x=25 \end{gathered}[/tex]