Respuesta :
Answer: (C) x = 9 is a true solution.
Step-by-step explanation: Edge 2021
x = 9 is a true solution to the equation [tex]\sqrt{x} -\sqrt{x-5} =1[/tex]
True solutions of equations
The given equation is:
[tex]\sqrt{x} -\sqrt{x-5} =1[/tex]
Rearrange the equation
[tex]\sqrt{x-5} = \sqrt{x} -1[/tex]
Square both sides
[tex]\sqrt{x-5}^2=(\sqrt{x} -1)^2 \\\\x-5=x-2\sqrt{x} +1\\\\2\sqrt{x} =1+5\\\\2\sqrt{x} =6[/tex]
Divide both sides by 2
[tex]\frac{2\sqrt{x} }{2}= \frac{6}{2} \\\\\sqrt{x} =3[/tex]
Square both sides
[tex]\sqrt{x} ^2=3^2\\\\x=9[/tex]
Therefore, the solution to the equation [tex]\sqrt{x} -\sqrt{x-5} =1[/tex] is x = 9
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