Need some help with math

[Sonic]

I have an equation here that I'm having trouble with. I'm not really good with math but what I basically need is the answer for "x".

Any help is greatly appreciated. Here is the equation

√ 3 - 3x = 5 + √ 3x + 2

 

[Sonic]

This actually for a friend who is having a bit of trouble. He came up with 18 but I have no clue if that is correct or not. If anyone could help that'd be real cool.

 

[akira888]

Is the "√ 3x" either:

1) sqrt(3*x)
or
2) sqrt(3)*x

edit: either way, how did he get 18 (?!) , unless I'm misreading something...

edit2: Assuming 2) the answer I derived is -1.11325. Obviously, I would double check that.

 

[Sonic]

3*x. I have no clue how he got 18.

 

[Xenus]

You sure the eqation isn't sqrt(3) - 3x = 5 + sqrt(3x + 2)

 

[Sonic]

I'm fairly positive. I'll let you know once I see the guy in about 20 minutes. I guess it would be a safe bet just to do this on the safe side.

 

[akira888]

The seems to be no answer for

 sqrt(3) - 3*x = 5 + sqrt(3 * x) +2

in the space of real numbers.

edit: I tried Xenus' recommendation as well, and again, I derived an imaginary result. Has your friend's class gone over the complex number space yet?

 

[Sonic]

Square root of "3-3x" = 5 + square root of "3x + 2"


I'm not sure how to put the sruare root sign over each equation, but if anyone can make that in math form it will be helpful.

Also, if it is bogus then that explains why he is having such a hard time with it.

 

[Xenus]

I got x = -8 but I might have done some "fuzzy math" when I tried to use FOIL to square the quantites.

sqrt(3 - 3x) = 5 + sqrt(3x + 2)


3x + 3x + 3 = 25 + 3x + 6x +2


6x + 3 = 25 + 9x + 2


-3x = 24

x = -8

 

[Silkworm]

(3-3x)^(1/2) = 5 + (3x+2)^(1/2)
remove the square root by squaring the entire eq.:

3-3x = 25 + 3x+2

group x's and the integers:
3x+3x = 3 - 25 -2
6x = -24
x = -4

 

[akira888]

Um, the square of 5 + (3x+2)^0.5 is 25 + 10 * sqrt(3x+2) + (3x+2), not 25 + (3x+2)

(a+b)^2 = a^2 + 2*a*b + b^2
(a+b)^2 != a^2 + b^2

 

[Xenus]

I looked a at it that way but it didn't seem right to me.

because

sqrt(3 - 3x) * sqrt(3 - 3x) = 3 + ( sqrt(3) * sqrt(3x) ) + ( sqrt(3) * sqrt(3x) ) + 3x

(a + b) ^ 2 = (a * a) + ( a * b) + (b * a) + (b * b)

 

[akira888]

Well craptastic. Once again, a pair of complex roots.

 

[Xenus]

Didn't you learn FOIL (first, outer, inner, last)

 

[Sonic]

So, does this mean there really is no solid number? Not even a fraction? He had a choice from these numbers.

2/3, 5 and 0, no solution

 

[akira888]

Oh dear, it's been ages since I took Algebra II. Let's see, 1992-1993. I'm old.

EDIT:

Sonic, are those four separate answers or two pairs of two correct answers?

EDIT 2:

The reason I ask is because I'm fairly certain there's no valid answer on the real number line. The domain is restricted to (-2/3,1); anything outside of that will generate complex numbers. Yet both square root terms only have a range of (0, sqrt(5)) on this domain, and therefore it should be impossible for the difference of the two to equal 5.

 

[Xenus]

Ah I see my mistake missing a negative sign. Damn my fuzzy math.

sqrt(3 - 3x) * sqrt(3 - 3x) = 3 + ( sqrt(3) * sqrt(3x) ) + ( sqrt(3) * sqrt(3x) ) + 3x

should be

sqrt(3 - 3x) * sqrt(3 - 3x) = 3 + ( sqrt(3) * sqrt(-3x) ) + ( sqrt(3) * sqrt(-3x) ) + 3x

 

[Sonic]

2/3. or two thirds.

5 and 0.

no solution

Those are the choices. Apparently he also needs inequalities which I told him he was on his own for. Thanks for all the help guys. This is for his college course and he is completely stumped. I wish I'd get more details but that doesn't seem to be the case, I will get some if I can.

 

[akira888]

Then the answer is "no solution," or at least not one on the real number line.

Just out of curiousity, what course is this?

 

[Xenus]

How did you get that I just tried it again and got 5.189 repeating but I give up I've gotten about 7 seperate answers 2 that have the possiblity of being correct 5.189 and 7.68.

Well my graphing calc. just told me it is a non-real answer so I guess I just did all that work for nothing.