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

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

Answer 2

Consider the equation:

$\sqrt{x+2}+4 = 8$

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

$\sqrt{x+2}+4-4= 8-4$

$\sqrt{x+2}= 4$

Squaring on both the sides of the equation, we get

$(\sqrt{x+2})^2 = (4)^2$

$x+2 = 16$

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.