Question

given the equation Square root of x minus 5 + 7 = 11 Solve for x and identify if it is an extraneous solution.

Answer 1

sqrt(x) - 5+7 =11
combine like terms
-5 +7 = 2

sqrt(x) + 2 = 11
subtract 2 from each side

sqrt(x) = 9

square both sides

x = 9^2

x = 81

an extraneous solution would be an invalid solution

in this case it is not an extraneous solution

Answer 2

x=21 and solution is not extraneous.

Explanation:

Given : Expression
`√((x-5))+7=11`

To find : The solution for x and identify if it is an extraneous solution?

Solution :

Expression
`√((x-5))+7=11`

`√((x-5))=11-7`

`√((x-5))=4`

Taking square both side,

`(√((x-5)))^2=4^2`

`x-5=16`

`x=21`

Substituting the value back in the equation to find this is an extraneous solution or not.

`√((21-5))+7=11`

`√((16))+7=11`

`4+7=11`

`11=11`

This is true.

Which means solution is not an extraneous solution.