 It is currently 23 Mar 2019, 23:19 ### GMAT 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

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # P = the product of all x-values that satisfy the  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS: GRE Instructor Joined: 10 Apr 2015
Posts: 1541
Followers: 56

Kudos [?]: 1466  , given: 8

P = the product of all x-values that satisfy the [#permalink]
1
KUDOS
Expert's post 00:00

Question Stats: 50% (02:03) correct 50% (03:39) wrong based on 8 sessions
P = the product of all x-values that satisfy the equation (x²)^(x² - 2x + 1) = x^(3x² + x + 8)
What is the value of P?

[Reveal] Spoiler:
0

_________________

Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Day emails Intern Joined: 26 Dec 2016
Posts: 4
Followers: 0

Kudos [?]: 7  , given: 0

Re: P = the product of all x-values that satisfy the [#permalink]
2
KUDOS
(x²)^(x² - 2x + 1) = x^(3x² + x + 8)
(x)^(2x² - 4x + 2) = x^(3x² + x + 8)
then, exponents are equal now,
2x² - 4x + 2 = 3x² + x + 8
-X^2 - 5X - 6 = 0
X^2 + 5X + 6 = 0
(X+2)(X+3)=0
thn, X= -2, and X= -3.
Also, X=0, X=1, and X= -1
P= -2*-3*0*1*-1=0 GRE Instructor Joined: 10 Apr 2015
Posts: 1541
Followers: 56

Kudos [?]: 1466  , given: 8

Re: P = the product of all x-values that satisfy the [#permalink]
4
KUDOS
Expert's post
GreenlightTestPrep wrote:
P = the product of all x-values that satisfy the equation (x²)^(x² - 2x + 1) = x^(3x² + x + 8)
What is the value of P?

[Reveal] Spoiler:
0

IMPORTANT: If b^x = b^y, then x = y, as long as b ≠ 0, b ≠ 1 and b ≠ -1
For example, if we have 1^x = 1^y, we cannot conclude that x = y, since 1^x equals 1^y FOR ALL values of x and y.
So, although 1² = 1³, we can't then conclude that 2 = 3.

So, let's first see what happens when the base (x) equals 0.

If x = 0, then we get: (0²)^(0² - 2(0) + 1) = 0^(3(0²) + 0 + 8)
Simplify: 0^1 = 0^8
Evaluate: 0 = 0
Perfect! We know that x = 0 is one solution to the equation.
This means the PRODUCT of all of the solutions will be ZERO, regardless of the other solutions.
In other words, P = 0

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Day emails Re: P = the product of all x-values that satisfy the   [#permalink] 28 Feb 2018, 13:00
Display posts from previous: Sort by

# P = the product of all x-values that satisfy the  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.