Please help.. questions due tonight by midnight.

[j9vo2]

1. solve by completing the square: -6x = 3x^2-2.. The answer I got for this is -3 +/- sqrt 3 divided by 3. is that correct?

2. solve: 1 +1/x = 12/x^2

3. simplify and rationalize the denominator: 8/[6+(2y)^1/2].. I guess the same thing would be 8/[6+ sqrt 2y]

4. solve: (w+16)^1/2 +4 = w ..same thing would be sqrt(w+16) +4 = w

5. solve: (x+6)^1/2 + x^1/2 = 3 ...same thing would be sqrt (x+6) + sqrt x = 3.

I cant find any information in my book how to solve these. Ive been trying to work them out for a couple of days now. any help would be greatly appreciated. thanks.

5.

 

[j9vo2]

I think I might have solved #5..

is the correct answer: 3/2.

this is how i got it..

sqrt (x+6) +sqrt 6 = sqrt 3

x+x 6 +9
2x+6 = 9
minus 6 from both sides to equal
2x=3
divide by 2 on both sides to equal
x =3/2

 

[Gene]

1) We can be more helpful if you show your work. Your answer is wrong.
-6x = 3x^2-2
3x^2+6x=2
x^2+2x=2/3
Complete the square by adding (b/2)^2 to both sides
x^2 +2x+1=2/3 + 1
Can you take it from there?

2) solve: 1 +1/x = 12/x^2
Multiply by x^2
x^2+x=12
x^2+x-12=0
Can you take it from there? It factors nicely. Always check your answers by substituting in the original equation.

3) Yes, the same thing would be
8/[6+ sqrt 2y]
Rationalize by multiplying by
(6-sqrt(2y))/(6-sqrt(2y))

4) Yes again
sqrt(w+16) +4 = w
sqrt(w+16) = (w-4)
Square both sides and solve the quadratic. Always check your answers by substituting in the original equation.

5. sqrt (x+6) + sqrt x = 3.
Get one sqrt by itself and square both sides.
sqrt (x+6) = 3 - sqrt (x)
x+6 = 9 - 6*sqrt(x) + x
Then do it again
Always check your answers by substituting in the original equation.

In your work:
I don't see where you got sqrt(3) on the RHS and
you can't square
sqrt (x+6) + sqrt(x) and get
(x+6)+x anymore than you can do (a+a)^2 and get a^2+a^2
Suppose x=3.
The first is 3+sqrt(3) but the second is
9+3
Not the same thing.

 

[j9vo2]

1. 3x^2 + 6x - 2 = 0
3x^2 + 6x + 3 = 5
x^2 + 2x + 1 = 5/3
(x+1)^2 = sqrt(5/3)
x+1 = +/-sqrt(5/3)
x = -1 +/- sqrt(5/3)

this is what i got but the answers don't correspond to any of the answers in my book.. what further steps do i need to take...

these are the answers..
-3 +/- sqrt3/3
[-3+/- (sqrt15)]/3
3+ sqrt3/3
[3+/- (sqrt15)]/2

would it be "B"...if i multiplied by 3???



2. is this correct?
1 + 1/x = 12/x^2
x^2 + x = 12
x^2 + x - 12 = 0
(x+4)(x-3) = 0
x = -4 or 3

3. is this correct?
8 / (6 + sqrt(2y)) =

<<< multiply top and bottom by 6 - sqrt(2y) >>>

8 * (6 - sqrt(2y) / [(6 +sqrt(2y))*(6 - sqrt(2y))]

(48 - 8sqrt(2y))/[36 - 2y]

<<<divide everything by 2>>>

(24 - 4sqrt(2y))/(18-y)


4. is the answer no solution for this one since I got 0

w - sqrt (w+16) + 4 = 0
(w+16) - sqrt(w+16) - 12 = 0
(sqrt(w+16) - 4)(sqrt(w+16) + 3) = 0
sqrt(w+16) = 4 (since it can't = -3)
w+16 = 16
w = 0


5. is this correct?
sqrt(x+6) + sqrt(x) = 3
sqrt(x+6) = 3 - sqrt(x)
<<square both sides>>
x+6 = 9 - 6sqrt(x) + x
6 = 9 - 6sqrt(x)
6sqrt(x) = 3
sqrt(x) = 1/2
x = 1/4

 

[j9vo2]

does anyone know if these are correct.. especially numbers 1 and 4

 

[Gene]

1) x = -1 +/- sqrt(5/3)
x = -1 +/- sqrt(15/9)
x = {-3 +/- sqrt(15)}/3

2) correct

3) I see no more simplification and it is right.

4) Reread my suggestion.
sqrt(w+16) +4 = w
sqrt(w+16)=w-4
w+16=w^2-8w+16
etc.

5) Looks good to me.