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Math Forum » Discussions » Math Topics » alt.algebra.help.independent

Topic: Help in two questions, please
Replies: 9   Last Post: Jan 31, 2012 8:48 AM

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HallsofIvy

Posts: 116
Registered: 1/19/06
Re: Help in two questions, please
Posted: Oct 26, 2009 10:10 PM
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> Hi!
>
> Here are two questions that have me really stumped.
>
> Q1 - If x + y = 2 and x^2 + y^2 = 8, find
>
> a) xy
> b) x - y
>
> Do I solve these simultaneously? Quadratically? Or
> something else?
Use the fact that (x+y)^2= x^2+ 2xy+ y^2. Since x+y= 2, (x+y)^2= 4. Since x^2+ y^2= 8, that equation becomes 4= 8+ 2xy.

For x-y, use the fact that (x-y)^2= x^2- 2xy+ y^2. You know that x^2+ y^2= 8 and you just found 2xy so you can find (x-y)^2 and then x- y.

>
> Q2 - Complete the sequence:
>
> 7/8, 2/3, 1/2, 4/11, 1/4, ______, ______ .
>
> I seriously can't figure out any pattern here!
>
> Thanks.

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