Respuesta :
x = -4 is the extraneous solution of the equation.
The equation is
(5 - x )^1/2 = x + 1
To find the extraneous solution first we need to find the value of x.
So we need to square on both sides of the equation
[tex](\sqrt{5- x})^{2}[/tex] = [tex](x + 1)^{2}[/tex]
5 - x = [tex]x^{2}[/tex] +2x + 1
[tex]x^{2}[/tex] + 3x - 4= 0
[tex]x^{2}[/tex] + 4x - x - 4 = 0
x( x + 4 ) - 1 ( x + 4) = 0
( x + 4)( x - 1) =0
x = -4, 1
Now put both the value of x in the solution in the equation.
x = -4
[tex]\sqrt{5 - (-4)}[/tex] = -4 + 1
[tex]\sqrt{9}[/tex] = -3
3≠ -3
Now put
x = 1
[tex]\sqrt{5 -1}[/tex] = 1 +1
[tex]\sqrt{4}[/tex] = 2
2 = 2
Therefore we get that x = -4 is the extraneous solution of the equation and x = 1 is the solution of the equation.
To know more about the extraneous solution of the equation refer to the link given below:
https://brainly.com/question/12361474
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