GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
equation with fourth root
[#permalink]
Updated on: 31 May 2019, 13:03
Updated on: 31 May 2019, 13:03
8
26
Bookmarks
00:00
Question Stats:
29% (01:34) correct
70% (01:32) wrong based on 256 sessions
Hide Show timer Statistics
\(x = \sqrt[4]{(x^3 + 6x^2)}\)
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
sum of all possible values of x |
1 |
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Originally posted by GreenlightTestPrep on 02 Feb 2019, 07:07.
Last edited by GreenlightTestPrep on 31 May 2019, 13:03, edited 2 times in total.
Last edited by GreenlightTestPrep on 31 May 2019, 13:03, edited 2 times in total.
Edited by Carcass
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: equation with fourth root
[#permalink]
03 Dec 2021, 06:19
03 Dec 2021, 06:19
2
1
1
Bookmarks
JKGrowling wrote:
This is incorrect the answer should be C.
(16)^1/2 has 2 solutions, 4 and -4
For a better representation, check the graphical representation of y = x^2. It is a parabola, with 2 x-intercepts(roots) centered around the y axis. The graph for y = x^4 is similar, except that is steeper because y rises faster than the run of x since it is a higher power.
(16)^1/2 has 2 solutions, 4 and -4
For a better representation, check the graphical representation of y = x^2. It is a parabola, with 2 x-intercepts(roots) centered around the y axis. The graph for y = x^4 is similar, except that is steeper because y rises faster than the run of x since it is a higher power.
Be careful, although there are two x-values (2 and -2) that satisfy the equation x^4 = 16, the fourth root notation tells us to take the positive root only.
So, ∜(16) = 2 (not -2)
If you want a graphical solution, it's better to graph the equation y = ∜x
If you do, you'll get something like this:
As you can see, there's only one value of y corresponding to x = 16
General Discussion
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: equation with fourth root
[#permalink]
02 Feb 2019, 07:09
02 Feb 2019, 07:09
11
1
4
Bookmarks
GreenlightTestPrep wrote:
x = ∜(x³ + 6x²)
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
sum of all possible values of x |
1 |
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Given: x = ∜(x³ + 6x²)
Raise both sides to the power of 4 to get: x⁴ = x³ + 6x²
Rewrite equation as follows: x⁴ - x³ - 6x² = 0
Factor to get: x²(x² - x - 6) = 0
Factor more to get: x²(x - 3)(x + 2) = 0
This means x² = 0, (x - 3) = 0, or (x + 2) = 0
So, the possible solutions are x = 0, x = 3 and x = -2
IMPORTANT: At this point, we should plug each answer choice back into the equation to identify any possible extraneous roots.
Test x = 0. We get: 0 = ∜(0³ + 6*0²) = ∜(0). WORKS
Test x = 3. We get: 3 = ∜(3³ + 6*3²) = ∜(81). WORKS
Test x = -2. We get: -2 = ∜(-2³ + 6*-2²) = ∜(16). DOESN’T work.
So, the only VALID solutions are x = 0 and x = 3
So, the SUM of all possible values of x = 0 + 3 = 3
We get:
QUANTITY A: 3
QUANTITY B: 1
Answer: A
Cheers,
Brent
