Last visit was: 19 Jul 2024, 04:50 It is currently 19 Jul 2024, 04:50
Toolkit
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.

# If x + 2/x = 3 what is the value of x^3 + 8/x^3 = ?

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94411
Own Kudos [?]: 642231 [0]
Given Kudos: 86282
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11475
Own Kudos [?]: 34436 [0]
Given Kudos: 322
General Discussion
Manager
Joined: 20 Aug 2017
Posts: 95
Own Kudos [?]: 206 [0]
Given Kudos: 174
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4918
Own Kudos [?]: 7806 [0]
Given Kudos: 221
Location: India
Re: If x + 2/x = 3 what is the value of x^3 + 8/x^3 = ? [#permalink]
Problems like these are the reason why I keep emphasizing on remembering the Algebraic identities. If you know algebraic identities, applying the appropriate one and solving this question will take you less than 30 seconds.

The algebraic identity to be used in this question is $$(a+b)^3$$ = $$a^3$$ + $$b^3$$ + 3ab(a+b).

In the problem given, x + $$\frac{2}{x}$$ = 3. We can take a = x and b = $$\frac{2}{x}$$; when we do this, we can quickly see that we are trying to find $$a^3$$ + $$b^3$$.
From the identity above, we see that $$a^3$$ + $$b^3$$ = $$(a+b)^3$$ – [3ab (a+b)].

Therefore, $$x^3$$ + $$(\frac{2}{x})^3$$ =$$(x+\frac{2}{x})^3$$ – [3 * x * $$\frac{2}{x}$$ (x + $$\frac{2}{x}$$)]. From the data given, x+$$\frac{2}{x}$$ = 3. Substituting and simplifying, we get,

$$x^3$$ + $$(\frac{2}{x})^3$$ = $$(3)^3$$ – [3*2(3)] = 27 – 18 = 9.

The correct answer option is C.

Hope that helps!
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 7999
Own Kudos [?]: 4239 [1]
Given Kudos: 243
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Re: If x + 2/x = 3 what is the value of x^3 + 8/x^3 = ? [#permalink]
1
Kudos
Bunuel wrote:
If $$x + \frac{2}{x} = 3$$ what is the value of $$x^3 + \frac{8}{x^3} =$$ ?

A. 1
B. 8
C. 9
D. 16
E. 18

solve for $$x + \frac{2}{x} = 3$$
we get a quadratic and value of x= 2 &1
so $$x^3 + \frac{8}{x^3} =$$
value = 9
IMO C
Re: If x + 2/x = 3 what is the value of x^3 + 8/x^3 = ? [#permalink]
Moderator:
Math Expert
94411 posts