Square Roots and x^2/3

[Melba]

First and foremost, I'm so glad I found this site. It is truly helpful...

I'm trying to see if I'm starting this problem correctly:

3x-2sqrtx-5=0.
First, divide -2 from 3x and -5 which would get you
3x/2-sqrtx-5/2=0
or do you want to isolate the squared term first?

I'm also having trouble with variables that have a 2/3 exponent/root. For ex:

x^2/3 - 6x^1/3=7

I did the problem like this:

x^2/3-6x^1/3-7=0
(x^1/3+1)(x^1/3-7)
x^1/3+1=0 or x^1/3-7=0
(x^1/3)^3=(-1)^3 or (x^1/3)^3=(7)^3 ---- I'm recepricating here...
so the final answer would be x=-1 or x=343

Yes, no?

 

[skeeter]

3x - 2sqrtx - 5 = 0

(3sqrtx - 5)(sqrtx + 1) = 0

finish?

be careful with extraneous roots.

 

[Deleted member 4993]

First and foremost, I'm so glad I found this site. It is truly helpful...

I'm trying to see if I'm starting this problem correctly:

3x-2sqrtx-5=0.

Substitute
\(\displaystyle u = sqrt{x}\)

\(\displaystyle u^2 = x\)

Then your equation turns to:

\(\displaystyle 3u^2 - 2u - 5 = 0\)

Solve by your favorite method to get

(3u - 5)(u + 1) = 0

Now solve, substitute back x in u, then check your solutions..




First, divide -2 from 3x and -5 which would get you
3x/2-sqrtx-5/2=0
or do you want to isolate the squared term first?

I'm also having trouble with variables that have a 2/3 exponent/root. For ex:

x^2/3 - 6x^1/3=7

I did the problem like this:

x^2/3-6x^1/3-7=0
(x^1/3+1)(x^1/3-7)
x^1/3+1=0 or x^1/3-7=0
(x^1/3)^3=(-1)^3 or (x^1/3)^3=(7)^3 ---- I'm recepricating here...
so the final answer would be x=-1 or x=343

Yes, no?

Check your solution by putting these values back into the originl equation - and check if those satisfy the given equation.

 

[Denis]

3x - 2sqrt(x) - 5 = 0.
First, divide -2 from 3x and -5 which would get you
3x/2 - sqrt(x) - 5/2 = 0
or do you want to isolate the squared term first?

Hey Melba; hope your last name is not Toast

NO, don't go dividing by 2!
YES, isolate: 3x - 5 = 2sqrt(x) ; now square both sides:
9x^2 - 30x + 25 = 4x
9x^2 - 34x + 25 = 0
(9x - 25)(x - 1) = 0
x = 25/9 or x = 1

Monsieurs Skeeter's and Khan's are equivalent to that.