Respuesta :
x = 6 is the extraneous solution of the equation
The equation given is
[tex]\sqrt{3x + 7}[/tex] = x -1
To find the Extraneous solution we need to square on both sides of the equation
[tex](\sqrt{3x + 7} )^{2}[/tex] =[tex](x - 1)^{2}[/tex]
3x + 7 = [tex]x^{2}[/tex] --2x + 1
[tex]x^{2}[/tex] - 5x - 6 = 0
[tex]x^{2}[/tex] - 6x + x - 6 = 0
x(x - 6) +1(x -6) =0
(x-6)(x+1) = 0
x = -1, 6
Now we need to put the value of x in the equation
x = -1
[tex]\sqrt{(3 * -1) + 7}[/tex] = -1 -1
[tex]\sqrt{4}[/tex] = -2
2≠ -2
Now put
x = 6
[tex]\sqrt{3 * 6 + 7}[/tex] = 6 -1
[tex]\sqrt{25}[/tex] = 5
5=5
Therefore we get to know that x = -1 is the extraneous solution 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
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