Respuesta :
-4 is an extraneous solution.
The equation is
[tex](x - 2)^{1/2}[/tex] - [tex](28-2x^{1/4}[/tex] = 0
To know whether the given equation has an extraneous solution or not we need to find the value of x.
[tex](x-2^{1/2}[/tex]= [tex](28-2x)^{1/4}[/tex]
Multiply both sides with the power of 4, and we get
[tex](x- 2)^{2}[/tex] = 28-2x
[tex]x^{2}[/tex] - 4x + 4 = 28-2x
[tex]x^{2}[/tex] - 2x - 24= 0
[tex]x^{2}[/tex]- 6x + 4x -24=0
x(x-6) +4(x-6)=0
(x-6)(x+4) = 0
x = 6 , -4
Now put both the value of x in the equation
x=6
[tex](6-2)^{1/2}[/tex]-[tex](28- 2* 6)^{1/4}[/tex]= 0
[tex]4^{1/2}[/tex]- [tex]16^{1/4}[/tex]= 0
2-2=0
0=0
Now
x = -4
[tex](-4-2)^{1/2}[/tex]-[tex](28-2*-4)^{1/4}[/tex]=0
[tex](-6)^{1/2}[/tex] -[tex]36^{1/4}[/tex]=0
[tex](-6)^{2}[/tex] - [tex]6^{1/2}[/tex]=0
Which is not possible and a negative integer is not present in the square root.
Therefore we get the extraneous solution of the equation which is x= -4, and x = 6 is the solution of the equation.
To know more about the extraneous solution refer to the link given below:
https://brainly.com/question/12361474