There is No Extraneous solution to the equation
The equation is
[tex]\sqrt{3x - 2}[/tex] - [tex]\sqrt{2x - 7}[/tex] = 0
We need to find the value of x,
[tex]\sqrt{3x + 2}[/tex] = [tex]\sqrt{2x + 7}[/tex]
Squaring both sides of the equation
[tex](\sqrt{3x + 2} )^{2}[/tex] = [tex](\sqrt{2x + 7} )^{2}[/tex]
3x + 2 = 2x + 7
x = 5
Now we need to put the value of x in the equation to know whether it is an extraneous solution or not.
[tex]\sqrt{(3 * 5 ) + 2}[/tex] - [tex]\sqrt{(2 * 5 ) + 7}[/tex] = 0
[tex]\sqrt{17}[/tex] - [tex]\sqrt{17}[/tex] = 0
0 = 0
Therefore we get to know that the equation has no extraneous solution.
To know more about the extraneous solution refer to the link given below:
https://brainly.com/question/12361474
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