If x,y,z are part of the set of reals where x <> y <> z, whose sum is zero and product is 2, find values of x^3 +y^3 + z^3.
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If x,y,z are part of the set of reals where x <> y <> z, whose sum is zero and product is 2, find values of x^3 +y^3 + z^3.
Geez how come i got -6?
so you didnt actually do it?
fine then and i think 91 was the answer to the one with the three roots right?
Prove it.Quote:
Originally posted by SilverSprite
Geez how come i got -6?
:D
x+y+z=0
xyz=2
(x+y+z)^3=0^3
Expand and get:
x^3+y^3+z^3+3xy^2+3xz^2+3yx^2+3zx^2+3yz^2+3zy^2+6xyz=0
Sub in xyz=2 to get:
x^3+y^3+z^3+3xy^2+3xz^2+3yx^2+3zx^2+3yz^2+3zy^2=12
Common factor:
x^3+y^3+z^3+3x^2 (y+z)+3y^2 (x+z)+3z^2 (x+y)=12
Sub solving for x,y,z in the first statment and subbing them back in then subtracting:
- 2x^3 - 2y^3 - 2z^3=12
Dividing both sides by -2 you get:
x^3+y^3+z^3=-6
Or that would work. And your right. And i'm not sure how you did it though.
Hey Silver, is it nice talking to yourself?
You might suffer a personality split.
...Oh, and you're too :)
Excuse me.
x^3 +y^3 + z^3 != (x+y+z)^3
(x+y+z)^3=(x+y+z)(x+y+z)(x+y+z) != x^3 +y^3 + z^3
Unless I'm not understanding the original question.
When I put in x^3+y^3+z^3 and x+y+z=0 and x*y*z=2 into my ti-92, it returns false.
And if x*y*z=2 then how can you get a negative result for them ^3? The signs would be the same. Thus the result would be a positive.
Wait. I know
-.9999... recurring, -1, 2
I get a positive 6.
:p
Yo Digital, I see you made a new nick.
Congratulations.
Sorry, I saw a small error involving the sub of xyz=2 that I Just had to fix.Quote:
Originally posted by SilverSprite
x+y+z=0
xyz=2
(x+y+z)^3=0^3
Expand and get:
x^3+y^3+z^3+3xy^2+3xz^2+3yx^2+3zx^2+3yz^2+3zy^2+6xyz=0
Sub in xyz=2 to get:
x^3+y^3+z^3+3xy^2+3xz^2+3yx^2+3zx^2+3yz^2+3zy^2=-12
Common factor:
x^3+y^3+z^3+3x^2 (y+z)+3y^2 (x+z)+3z^2 (x+y)=-12
Sub solving for x,y,z in the first statment and subbing them back in then subtracting:
- 2x^3 - 2y^3 - 2z^3=-12
Dividing both sides by -2 you get:
x^3+y^3+z^3=6
;)
-Lou
My mistake ;)
what happened to the really nice proof that got the answer in three lines? ;)