System

**Apprentice123** · December 12th 2008, 09:36 AM

Solve:

$x^3-y^3=602$
$xy(y-x)=-198$

Answer:
x = 11 and y = 9
or
x = -9 and y = -11

**Chop Suey** · December 12th 2008, 10:00 AM

I will give you two hints:

$(x-y)^3 = x^3 - 3x^2y + 3xy^2 - y^3$

$xy^2 - x^2y=-198 \implies -3x^2y+3xy^2=-594$

**Apprentice123** · December 12th 2008, 10:14 AM

How i find the answer ?

**Chop Suey** · December 12th 2008, 10:20 AM

$x^3-y^3=602$

$-3x^2y+3xy^2=-594$

If we combine the two expressions, we get a perfect cube:
$x^3 - 3x^2y+3xy^2-y^3=602-594 \implies (x-y)^3=8 \implies x - y =\ldots$

This is your key to solving for x and y. Can you do it now?

**Apprentice123** · December 12th 2008, 10:36 AM

thank you

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