Question

Find the solution of square root x+2+4=8 , and determine if it is an extraneous solution-x = 14; extraneousX = 58; extraneousx = 14; not extraneousx = 58; not extraneous

Answer 1

At first, let us solve The equation

`√(x+2)\text{ +4 - 4 = 8 - 4}`

We will subtract 4 from both sides

`√(x+2)=4`

Then let us square both sides

`x+2=(4)^2\text{ }`
`x\text{ + 2 = 16}`

Subtract 2 from both sides to get the value of x

`x\text{ = 14}`

You have two choices with 14

Which one will you choose?

To answer this you must know does this value including the domain or not

Let us try this value for x in the equation if the left-hand side equals the right-hand-side then the value is not extraneous

`left-handside\Rightarrow\sqrt{14\text{ + 2}}+4=√(16)+4=4\text{ +4 =8}`

Since the right-hand side has the same value, so 14 is not extraneous.

So the correct answer is the third choice.