Answer:
Solution: x = 6
Step-by-step explanation:
Given equation is:
[tex]\sqrt{2x+8}=6[/tex]
In order to solve the equation both sides will be squared
[tex](\sqrt{2x+8})^{2} = (6)^2 \\2x+8 = 36\\2x = 36-8\\2x = 28\\x = 14[/tex]
Verifying the solution
[tex]\sqrt{2(14)+8} = 6\\ \sqrt{28+8} = 6\\\sqrt{36} = 6\\6 = 6[/tex]
Answer:
No extraneous solution
Step-by-step explanation:
The given equation is
[tex]\sqrt{2x+8}=6[/tex]
Taking square on both sides.
[tex](\sqrt{2x+8})^2=(6)^2[/tex]
[tex]2x+8=36[/tex]
Subtract 8 from both sides.
[tex]2x+8-8=36-8[/tex]
[tex]2x=28[/tex]
Divide both sides by 2.
[tex]x=14[/tex]
The solution of given equation is 14.
The solutions of an equation are known as extraneous solutions if they are invalid.
Substitute x=14 in the given equation.
[tex]\sqrt{2(14)+8}=6[/tex]
[tex]\sqrt{36}=6[/tex]
[tex]6=6[/tex]
LHS=RHS, so x=14 is a valid solution.
Therefore, the given equation have no extraneous solution.
