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# If 8xy^3 + 8x^3*y=2x^2*y^2/ 2^-3,what is the value of x?

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If 8xy^3 + 8x^3*y=2x^2*y^2/ 2^-3,what is the value of x? [#permalink]  24 Dec 2012, 05:18
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If $$8xy^3 + 8x^3y=\frac{2x^2y^2}{2^{-3}}$$ , what is the value of xy?

(1) y > x
(2) x < 0
[Reveal] Spoiler: OA

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Re: If 8xy^3 + 8x^3*y=2x^2*y^2/ 2^-3,what is the value of x? [#permalink]  24 Dec 2012, 05:32
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If $$8xy^3 + 8x^3y=\frac{2x^2y^2}{2^{-3}}$$, what is the value of xy?

$$8xy^3 + 8x^3y=\frac{2x^2y^2}{2^{-3}}$$ --> $$8xy^3 + 8x^3y=8*2x^2y^2=0$$ --> reduce by 8 and re-arrange: $$xy^3+x^3y-2x^2y^2$$ --> factor out xy: $$xy(y^2+x^2-2xy)=0$$ --> $$xy(y-x)^2=0$$ --> $$xy=0$$ or $$y-x=0$$.

(1) y > x. Since $$y>x$$, then $$y-x\neq{0}$$, thus $$xy=0$$. Sufficient.

(2) x < 0. Not sufficient.

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Re: If 8xy^3 + 8x^3*y=2x^2*y^2/ 2^-3,what is the value of x? [#permalink]  25 Dec 2012, 12:18
Bunuel wrote:
If $$8xy^3 + 8x^3y=\frac{2x^2y^2}{2^{-3}}$$, what is the value of xy?

$$8xy^3 + 8x^3y=\frac{2x^2y^2}{2^{-3}}$$ --> $$8xy^3 + 8x^3y=8*2x^2y^2=0$$ --> reduce by 8 and re-arrange: $$xy^3+x^3y-2x^2y^2$$ --> factor out xy: $$xy(y^2+x^2-2xy)=0$$ --> $$xy(y-x)^2=0$$ --> $$xy=0$$ or $$y-x=0$$.

(1) y > x. Since $$y>x$$, then $$y-x\neq{0}$$, thus $$xy=0$$. Sufficient.

(2) x < 0. Not sufficient.

if y>x then xy can't be equal 0. It can't be discussed.
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Re: If 8xy^3 + 8x^3*y=2x^2*y^2/ 2^-3,what is the value of x? [#permalink]  26 Dec 2012, 02:43
Expert's post
akshin wrote:
Bunuel wrote:
If $$8xy^3 + 8x^3y=\frac{2x^2y^2}{2^{-3}}$$, what is the value of xy?

$$8xy^3 + 8x^3y=\frac{2x^2y^2}{2^{-3}}$$ --> $$8xy^3 + 8x^3y=8*2x^2y^2=0$$ --> reduce by 8 and re-arrange: $$xy^3+x^3y-2x^2y^2$$ --> factor out xy: $$xy(y^2+x^2-2xy)=0$$ --> $$xy(y-x)^2=0$$ --> $$xy=0$$ or $$y-x=0$$.

(1) y > x. Since $$y>x$$, then $$y-x\neq{0}$$, thus $$xy=0$$. Sufficient.

(2) x < 0. Not sufficient.

if y>x then xy can't be equal 0. It can't be discussed.

You should read a solution carefully.

From the stem we have that either $$xy=0$$ or $$y-x=0$$.

(1) says that y > x, so y - x > 0, which means that $$y-x\neq{0}$$, thus $$xy=0$$.
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Re: If 8xy^3 + 8x^3*y=2x^2*y^2/ 2^-3,what is the value of x? [#permalink]  28 Mar 2015, 20:49
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Re: If 8xy^3 + 8x^3*y=2x^2*y^2/ 2^-3,what is the value of x?   [#permalink] 28 Mar 2015, 20:49
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