Question

Find the solution of the square root of the quantity of x plus 2 plus 4 equals 8, and determine if it is an extraneous solution

Answer 1

`\bf √(x+2)+4=8\implies √(x+2)=8-4\implies √(x+2)=4 \\\\\\ x+2=16\implies x=16-2\implies x=14\impliedby \begin{array}{llll} doesn't\ look\\ extraneous \end{array}`

Answer 2

Consider the equation:

`√(x+2)+4 = 8`

Subtracting '4' from both the sides of the equation, we get as

`√(x+2)+4-4= 8-4`

`√(x+2)= 4`

Squaring on both the sides of the equation, we get

`(√(x+2))^2 = (4)^2`

`x+2 = 16`

Subtracting '2' from both the sides of the equation, we get

`x+2-2=16-2`

x=14

Since, An extraneous solution is a solution that arises from the solving process that is not really a solution at all. But, in this equation x=14 is the solution of the given equation.

Hence, it is not an extraneous solution.