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# P = the product of all x-values that satisfy the

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GRE Instructor
Joined: 10 Apr 2015
Posts: 1541
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Kudos [?]: 1466 [1] , given: 8

P = the product of all x-values that satisfy the [#permalink]  09 Jan 2017, 12:02
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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

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Joined: 26 Dec 2016
Posts: 4
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Kudos [?]: 7 [2] , given: 0

Re: P = the product of all x-values that satisfy the [#permalink]  23 Jan 2017, 01:35
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 [4] , given: 8

Re: P = the product of all x-values that satisfy the [#permalink]  28 Feb 2018, 13:00
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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

Re: P = the product of all x-values that satisfy the   [#permalink] 28 Feb 2018, 13:00
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# P = the product of all x-values that satisfy the

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