Answer:
[tex]x=1[/tex]
Step-by-step explanation:
We have been given an equation [tex]\sqrt{x+3}+4=6[/tex]. We are asked to find the solution of our given equation.
[tex]\sqrt{x+3}+4-4=6-4[/tex]
[tex]\sqrt{x+3}=2[/tex]
Now, we will square both sides of our given equation.
[tex]x+3=2^2[/tex]
[tex]x+3=4[/tex]
[tex]x+3-3=4-3[/tex]
[tex]x=1[/tex]
To see whether [tex]x=1[/tex] is an extraneous solution or not, we will substitute [tex]x=1[/tex] in our given equation as:
[tex]\sqrt{1+3}+4=6[/tex]
[tex]\sqrt{4}+4=6[/tex]
[tex]2+4=6[/tex]
[tex]6=6[/tex]
Since both sides of our given equation are equal, therefore, [tex]x=1[/tex] is a solution for our given equation.
