Quite tricky, and untypical math question: functions/polynom

Discus: SAT/ACT Tests and Test Preparation: March 2004 Archive: Quite tricky, and untypical math question: functions/polynom
 By Jszab (Jszab) on Wednesday, March 03, 2004 - 12:33 pm: Edit

W(0)=2
W(x1+x2) = W(x1)+W(x2) + 2x1x2 - 2

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What do you think about way of putting somethings, and than make linked equations?

for example:
W(x+x)
W(x-x)
and so on.

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 By Averagemathgeek (Averagemathgeek) on Wednesday, March 03, 2004 - 11:37 pm: Edit

I found a solution:
W(x-x)=W(x)+W(-x)-2x^2-2
W(x)+W(-x)=2x^2+4
This is where I went with my instincts: I assumed the function was even.
2W(x)=2x^2+4
W(x)=x^2+2

Here is the verification:
W(0)=0^2+2=2
W(x+y)=(x+y)^2+2=x^2+y^2+2xy+2
=x^2+2+y^2+2-4+2xy+2
=W(x)+W(y)+2xy-2

Hope this helps.

 By Jszab (Jszab) on Thursday, March 04, 2004 - 02:50 am: Edit

proof by example ;). Ok.
I'll try to find a proof for thesis it is even function. I am thinking by now about x^2+2 as an unchangable constant, independant from sign of unknowns.

Thank You very much indeed. Actually I had not tried with this question. I hope, that it helped You.

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