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

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

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New post 02 Jun 2019, 04:26
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Question Stats:

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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

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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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New post 02 Jun 2019, 05:00
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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
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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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New post 09 Jun 2019, 11:12
LeoN88 Im not sure if I catched your idea. Could you please elaborate?
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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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New post 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.
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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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New post 09 Jun 2019, 21:58
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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.

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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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