Answer:
D. [tex]c-2=25+c+10\sqrt{c}[/tex]
Step-by-step explanation:
We have been given a radical equation [tex]\sqrt{c-2}-\sqrt{c}=5[/tex]. We are asked to find the equation that results from isolating a radical term and squaring both sides of the equation for the equation.
Add [tex]\sqrt{c}[/tex] on both sides:
[tex]\sqrt{c-2}-\sqrt{c}+\sqrt{c}=5+\sqrt{c}[/tex]
[tex]\sqrt{c-2}=5+\sqrt{c}[/tex]
Square both sides:
[tex](\sqrt{c-2})^2=(5+\sqrt{c})^2[/tex]
Using radical rule [tex]\sqrt[n]{a^n} =a[/tex], we will get:
[tex]c-2=(5+\sqrt{c})^2[/tex]
Using perfect square formula [tex](a+b)^2=a^2+2ab+b^2[/tex], we will get:
[tex]c-2=5^2+2*5\sqrt{c}+(\sqrt{c})^2[/tex]
[tex]c-2=25+10\sqrt{c}+c[/tex]
[tex]c-2=25+c+10\sqrt{c}[/tex]
Therefore, option D is the correct choice.
