Radical Equation: square root of x+2, +1 = square root of x+

M

moname

New member
Joined
May 3, 2009
Messages
7
square root of x+2, +1 = square root of x+4

1. subtract 1 from both sides to get to isolate left side of equation.
2. multiply each side of equation 2nd power square root of x+2 (squared) + square root of x+4, -1 squared?
3. that leaves x + 2 = x + 3?
Not sure....the answer is -7/4, but have no idea how that was achieved.

I am an older student getting my BA in Sociology, and I so appreciate your help.

Thank you.
 


I looks to me like you subtracted the 1 from the 4 before squaring.

We cannot do that because the 4 is part of the square root expression and the 1 is not.

We type square roots as sqrt(x + 4).

Your given equation is:

sqrt(x + 2) + 1 = sqrt(x + 4)

It's not really necessary to subtract the 1 first (since we need to square both sides, anyway), but I'll go with that.

sqrt(x + 2) = sqrt(x + 4) - 1

Now, we square both sides to get rid of the radical on the lefthand side.

[sqrt(x + 2)]^2 = [sqrt(x + 4) - 1]^2

You squared the lefthand side, correctly.

x + 2 = [sqrt(x + 4) - 1]^2

The righthand side means [sqrt(x + 4) - 1] * [sqrt(x + 4) - 1].

The expression sqrt(x + 4) - 1 is two terms. We can square this expression using a process known as FOIL.

Are you familiar with FOIL? Symbolically, it looks like this:

(A - B)^2 = A^2 - AB - AB + B^2

After combining like terms, the squared result is A^2 - 2AB + B^2.

With this symbolism, A represents your sqrt(x + 4) term, and B represents 1.

So, you can square sqrt(x + 4) -- that's the A^2 part.

You can multiply sqrt(x + 4) times -1, and double the result -- that's the -2AB part.

You can square -1 -- that's the B^2 part.

Then combine these results.

Here's an example of using FOIL to square a similar expression with two terms.

[sqrt(x - 3) + 5]^2 = [sqrt(x - 3) + 5] * [sqrt(x - 3) + 5]

Using FOIL, I start by multiplying sqrt(x - 3) times sqrt(x - 3) to get x - 3.

Next, I multiply sqrt(x - 3) times -1 to get -sqrt(x - 3).

Next, I multiply -1 times sqrt(x - 3) to get -sqrt(x - 3), again.

Lastly, I multiply -1 times -1 to get 1.

Putting it all together gives:

x - 3 - sqrt(x - 3) - sqrt(x - 3) + 1

Combining like terms, yields:

x - 3 - 2*sqrt(x - 3) + 1

Now, you try.

After you properly square the righthand side, you'll still have a radical. Move all of the other term to the lefthand side, in order to isolate this radical, and then square the resulting equation a second time.

You should end up with the following result, after square a second time.

x + 4 = 9/4

Let us know if you need more help. Please show your work, so that we might determine where to continue helping you.

If my post is too confusing, let me know. I will look for some web sites that give lessons on this.

Cheers 8-)

 
Thanks so much for your help. You were right - I subtracted the "1" prematurely and included in as part of the term rather than a stand alone coefficient. I used your format and instruction to do a similar problem and I got the correct answer. You are wonderful and I appreciate your time, help, patience AND the websites.

Have a good week,

Mo... :D
 


You're welcome.

I forgot to mention an important point.

Anytime we decide to square both sides of an equation, during the solution process, it's very important to verify our end results because the act of squaring sometimes introduces "false" solutions.

By substituting result(s) back into the original equation, we can verify that they lead to a true statement.

I realize that you had the solution confirmed for you in advance, but this will not always be so.

Plus, it'll help satisfy the craving that you dream about over doing extra algebra practice by hand. :wink:

sqrt(-7/4 + 2) + 1 = sqrt(-7/4 + 4)

sqrt(1/4) + 1 = sqrt(9/4)

1/2 + 1 = 3/2

3/2 = 3/2

A true statement.

 
Thanks for the reminder, but since math is not my forte, I always check, which is why I knew I got the correct answer for the second problem....and you're right, math practice is right on top of my craving list, along with dentist visits, flat tires in the snow, and warts on my chin. Thanks for helping me satiate at least one :lol: ! Take care, have a great week and until my next assignment brain fog!
 
You must log in or register to reply here.
Top