crack dat math question

[msu08]

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if x+y=3 and x^2+y^2= 8 than what is the value of xy?
the answer is .5 and the explanation they give makes absolutely no sense to me. any ideas??

 

[Streetwolf]

if x+y=3 and x^2+y^2= 8 than what is the value of xy?
the answer is .5 and the explanation they give makes absolutely no sense to me. any ideas??

if x+y = 3 then (x+y)^2 = 3^2 = 9. Since (x+y)^2 is really x^2 + 2xy + y^2, then x^2 + 2xy + y^2 = 9. When you rearrange the terms on the left, you have x^2 + y^2 + 2xy = 9.

We also know that x^2 + y^2 = 8 (given to us by the problem). So we can substitute this into our equation above:

8 + 2xy = 9

Thus 2xy = 1 and so xy = 1/2.

 

[suhshi]

if x+y = 3 then (x+y)^2 = 3^2 = 9. Since (x+y)^2 is really x^2 + 2xy + y^2, then x^2 + 2xy + y^2 = 9. When you rearrange the terms on the left, you have x^2 + y^2 + 2xy = 9.

We also know that x^2 + y^2 = 8 (given to us by the problem). So we can substitute this into our equation above:

8 + 2xy = 9

Thus 2xy = 1 and so xy = 1/2.

THANKS streetwolf

 

[joedat41]

i also had toruble with that problem. now it makes a lot of sense thanks.

 

[illbirz]

OH WOW...so u cant just solve for one variable for example X and then plug it in the other equation to get one and consequently the other. hhhmm...i c

 

[Streetwolf]

OH WOW...so u cant just solve for one variable for example X and then plug it in the other equation to get one and consequently the other. hhhmm...i c

No, you can. And you'd get an answer too. You'd get [3 +- sqrt(7)] / 2 (one of them is x and the other is y). When you multiply (3 + sqrt7)/2 and (3 - sqrt7)/2 together, you get 1/2.