-2 is the extraneous solution of the equation.
The equation is:
[tex](x + 3)^{1/2}[/tex] - 1 = x
To find the extraneous solution of the expression first we need to find the value of x.
[tex](x + 3)^{1/2}[/tex] = x + 1
Squaring both sides we have,
[tex](x+ 3)^{}[/tex] = [tex](x + 1)^{2}[/tex]
x + 3 = [tex]x^{2}[/tex] + 2x + 1
[tex]x^{2}[/tex] + x - 2 = 0
[tex]x^{2}[/tex] + 2x - x - 2 = 0
x ( x + 2 ) - 1 (x + 2) = 0
(x+2) (x-1)=0
x = -2, 1
Now we have to put the value of x in the equation:
x = -2
[tex](-2 +3)^{1/2}[/tex] - 1 = -2
1-1 =-2
0≠ -2
x = 1
[tex](1 + 3)^{1/2}[/tex] - 1= 1
2 - 1 = 1
1= 1
Therefore we get x = -2 is as extraneous solution of the equation and x= 1 is the solution of the equation.
To know more about the extraneous solution refer to the link given below:
https://brainly.com/question/12361474
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