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# Find the value of x3 + 8y3 + z3 in terms of x, y and z if x

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Intern
Joined: 14 Oct 2018
Posts: 18
Find the value of x3 + 8y3 + z3 in terms of x, y and z if x  [#permalink]

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02 Jun 2019, 04:26
3
00:00

Difficulty:

85% (hard)

Question Stats:

38% (01:46) correct 62% (02:31) wrong based on 50 sessions

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Find the value of x^3 + 8y^3 + z^3 in terms of x, y and z if x + 2y + z = 0?

A) 6xyz
B) 8xyz
C) -24x(y+z)
D) 3(xy+zx+yz)
E) None of the above

Posted from my mobile device
ISB School Moderator
Joined: 08 Dec 2013
Posts: 643
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB
GMAT 1: 630 Q47 V30
WE: Operations (Non-Profit and Government)
Re: Find the value of x3 + 8y3 + z3 in terms of x, y and z if x  [#permalink]

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02 Jun 2019, 05:00
2
Rajat1998 wrote:
Find the value of x^3 + 8y^3 + z^3 in terms of x, y and z if x + 2y + z = 0?

A) 6xyz
B) 8xyz
C) -24x(y+z)
D) 3(xy+zx+yz)
E) None of the above

Posted from my mobile device

a^3 + b^3 + c^3 -3abc = (a+b+c)(a^2+b^2+c^2 -ab-bc-ca)
x^3 + 8y^3 + z^3 - 3(x*2y*z) = 0.

So required= 6xyz
Intern
Joined: 18 Aug 2018
Posts: 12
Location: Turkey
Concentration: Strategy, Technology
GPA: 3.31
Re: Find the value of x3 + 8y3 + z3 in terms of x, y and z if x  [#permalink]

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09 Jun 2019, 11:12
LeoN88 Im not sure if I catched your idea. Could you please elaborate?
ISB School Moderator
Joined: 08 Dec 2013
Posts: 643
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB
GMAT 1: 630 Q47 V30
WE: Operations (Non-Profit and Government)
Re: Find the value of x3 + 8y3 + z3 in terms of x, y and z if x  [#permalink]

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09 Jun 2019, 21:08
elifceylan wrote:
LeoN88 Im not sure if I catched your idea. Could you please elaborate?

a^3 + b^3 +c^3 -3abc = (a+b+c)(a^2 + b^2 +c^2 -ab-bc-ca)...This is a formula

Now given:x^3 + (2y)^3 + z^3 - 3(2xyz) = 0 because (x+2y+z) is zero, zero*anything is zero.

x^3 + (2y)^3 + z^3 - 3(2xyz) = 0

x^3 + (2y)^3 + z^3 = 6xyz.
elifceylan
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Joined: 20 Jul 2017
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Re: Find the value of x3 + 8y3 + z3 in terms of x, y and z if x  [#permalink]

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09 Jun 2019, 21:58
2
1
Rajat1998 wrote:
Find the value of x^3 + 8y^3 + z^3 in terms of x, y and z if x + 2y + z = 0?

A) 6xyz
B) 8xyz
C) -24x(y+z)
D) 3(xy+zx+yz)
E) None of the above

Posted from my mobile device

Given x + 2y + z = 0
—> x + z = -2y
Cube on both sides
—> (x + z)^3 = (-2y)^3
—> x^3 + z^3 + 3xz(x + z) = -8y^3
—> x^3 + 8y^3 + z^3 = -3xz(x + z) = -3xz(-2y) {Given x + 2y + z = 0}
—> x^3 + 8y^3 + z^3 = 6xyz

IMO Option A.

Pls Hit kudos if you like the solution
Re: Find the value of x3 + 8y3 + z3 in terms of x, y and z if x   [#permalink] 09 Jun 2019, 21:58
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