PLEAAASE Help Me Check This Answer

ProfessorFilostrato said:
Solve the equation and check for extraneous solutions. (x + 2) =x

I got x = 2 and x = -1

Am I right???
Click to expand...
Did you check your answers?

Let's try x=2

(2+2) = 2 ????
4 = 2 ???? Nope.

Let's try x = -1

(-1+2) = -1 ????
1 = -1 ???? Nope.

Now, let's try solving.

x + 2 =x

Subtract x from both sides:

2 = 0 -- Well, that's an unfortunate result. No solutions.

How did you get 2 and -1??
 
TkHunny, ARGH! I mistyped the problem! It was not (x + 2) = x It was the square root of(x + 2) = x I imput 2 into that equation amd get 2 + 2 = 4. Square root of 4 is 2. So x is 2. But I am still not sure if -1 is also an answer. Any help would be great! :wink:
 
ProfessorFilostrato said:
square root of(x + 2) = x
Click to expand...
Ah, that's a little different.

First, very first, before anything else, is Domain considerations.

sqrt(x+2) <== In order for this to existin the Real numbers, x+2 >= 0, or x >= -2.

Now, we have a whole patch of Real numbers that we won't even have to try. If we get x = -3, we'll just throw it out. Don't even bother to check it.

Further, sqrt(x+2), by convetion, means the Positive square root. It does NOT mean +/- anything. Thus, with a bit of ponder that I'll let you do, x >= 0. We managed to narrow down the Domain a bit more. Negative values WILL NOT do. Don't even bother th check them.

sqrt(x+2) = x

Square both sides (a risky business)

x+2 = x^2
x^2 - x - 2 = 0
(x-2)(x+1) = 0
x = 2 or x = -1

Only x = 2 is in the Domain, so let's check it in the ORIGINAL equation.

sqrt(2+2) = 2 ???
sqrt(4) = 2 ???
2 = 2 Check

Done.

If you would like to check x = -1, you may, bet we know already that it won't work.

sqrt(-1+2) = -1 ???
sqrt(1) = -1 ???
1 = -1 Nope - That's no good.

Did I mention how important the Domain consideration were?
 
You must log in or register to reply here.
Top