√x-3 + √x = 3 more simple algebra

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In summary, the conversation was about solving the equation √x-3 + √x = 3 using algebra. The solution was found to be x=4, and the steps involved expanding and simplifying the equation. The process involved distributing and combining terms to get to the final solution.
  • #1
viet_jon
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[SOLVED] √x-3 + √x = 3 more simple algebra

Homework Statement



√x-3 + √x = 3

( √x-3 + √x ) ( √x-3 + √x ) = 9


The Attempt at a Solution



I have the answer in my book as x=4 , but I don't understand how they got there.

these are the next two steps which I don't understand, everything after I get so I didn't type it here.

(x-3) + 2√x-3 √x + x = 9

2x - 3 + 2√x²-3x = 9
* the -3x is in the square root
 
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  • #2
(x-3) + 2√x-3 √x + x = 9

you got this by expanding out ( √x-3 + √x ) ( √x-3 + √x )

if you take everything else except the sq.root on the other side(with the 9) you'll get
[itex]\sqrt{x^2-3x}=(6-x)[/itex] then just square both sides and expand again
 
  • #3
man I don't know what you mean. how do you expand out?
 
  • #4
Just as in any (a + b)(a + b), you distribute appropriately.

(a + b)(a + b) = (a + b)(a) + (a + b)(b)

= (a)(a) + (b)(a) + (a)(b) + (b)(b).

That's all "expand" means.
 
  • #5
varygoode said:
Just as in any (a + b)(a + b), you distribute appropriately.

(a + b)(a + b) = (a + b)(a) + (a + b)(b)

= (a)(a) + (b)(a) + (a)(b) + (b)(b).

That's all "expand" means.



so everytime I have (a + b)(a + b) this is all I have to do is put it in the form you wrote up there? is there anything else I need to know about this?

what is this called anyway? a lot of questions i know, sorry...it's just I want to understand it, rather than just memorizing how to do it.
 
  • #6
It's just simple distribution. No special name (that I can think of off the top of my head).

As long as you know what it means to distribute, i.e.:

a(b + c) = ab + ac.
 
  • #7
it still doesn't add up.

how does (√x-3 + √x) (√x-3 + √x) = 9

distributed into form (a)(a) + (b)(a) + (a)(b) + (b)(b)

= (x-3) + 2√x-3 √x + x = 9 ?


wouldn't it be... (√x-3)(√x-3) + (√x)(√x-3) + (√x-3)(√x) + (√x)(√x) ?
 
  • #8
Your last expression isn't completely simplified.

[tex] (\sqrt{x-3})(\sqrt{x-3}) = x-3 [/tex]

[tex] (\sqrt{x})(\sqrt{x}) = x [/tex]

And, finally, there are two of the term:

[tex] (\sqrt{x-3})(\sqrt{x}) [/tex]

(which is the same as:)

[tex] (\sqrt{x})(\sqrt{x-3}) [/tex]

which need combining.

That should resolve that particular issue.
 
  • #9
dude...I'm even more lost now. I hate to admit that. I use to be one of the top math students, now I'm struggling with grade 11 crap.
 
  • #10
i hate to keep bothering ya, but I read your last post no less than 20x, and I still don't understand how it works.
 
  • #11
wait...nm...i got it now...

thnkx a lot brother...owe u 1
 
  • #12
Oh, great! Not a problem.

I had started writing a more detailed and fancy response for you, but now I don't need to. Thanks!

Post again if you have any more questions!

P.S.: Instead of triple-posting, try editing your first post next time. :)
 

1. What is the purpose of "√x-3 + √x = 3" in algebra?

The purpose of this equation is to solve for the value of x. In algebra, equations are used to represent relationships between variables, and by solving for x, we can determine the specific value that satisfies this particular equation.

2. How can I simplify "√x-3 + √x = 3" to make it easier to solve?

To simplify this equation, we can first combine the two square root terms by using the property √a + √b = √(a + b). This gives us √x-3 + √x = √(x - 3 + x) = √(2x - 3) = 3. From here, we can square both sides of the equation to get rid of the square root and then solve for x.

3. Can this equation be solved using basic algebraic principles?

Yes, this equation can be solved using basic algebraic principles such as combining like terms, using properties of square roots, and isolating the variable on one side of the equation.

4. What are the possible values of x that satisfy "√x-3 + √x = 3"?

The possible values of x that satisfy this equation depend on the domain of the square root function. In this case, since the equation includes the term √(x - 3), x must be greater than or equal to 3 in order for the square root to be a real number. Therefore, the possible values of x are all real numbers greater than or equal to 3.

5. Are there any real-life applications of "√x-3 + √x = 3"?

Yes, this equation can be used to model real-life situations involving square roots, such as finding the length of one side of a right triangle given the other two sides, or calculating the speed of an object based on its kinetic energy. It can also be used in physics and engineering to solve for unknown variables in various equations.

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