Question

i am stuck on the following if x^2-y^2=a and x-y=b, then what does x^2+y^2=

Answer 1

the suspense is killing me

Answer 2

:o)

Answer 3

aw

Answer 4

Difference of squares
x^2 - y^2 = (x+y)(x-y)
a = b*(x+y) --> x+y = a/b

haha
sorry got stuck here

Answer 5

yeah...

Answer 6

so what does x^2 + y^2 equal again?

Answer 7

lol i think

Answer 8

wait isn't it (a/b)^2

Answer 9

because
\[\frac{a}{b}=(x+y)\] so
\[(\frac{a}{b})^2=(x+y)^2=x^2+y^2+2xy\]

Answer 10

i mean that is why it is not (a/b)^2

Answer 11

\[x^2-y^2=a =>x^2=a+y^2\]
\[x-y=b=>x=b+y=>x^2=(b+y)^2=b^2+2by+y^2\]
\[b^2+2by+y^2=a+y^2=b^2+2by=a=>a-b^2=2by=>y=\frac{a-b^2}{2b}\]
but we have
\[x^2=a+y^2=>x^2+y^2=a+y^2+y^2=a+2y^2=a+2 \cdot (\frac{a-b^2}{2b})^2\]

Answer 12

the answer choices are
a. 2xy
b. -2xy
c. (a/b)^2 +2xy
d. (a/b)^2-2xy
e. (a/b) - xy

Answer 13

Thanks for everyone's thoughts on this, it is really confusing me

Answer 14

the answer choices would have been helpful in the begining lol

Answer 15

lol

Answer 16

I know, sorry about that

Answer 17

d

Answer 18

That's why I meant, I meant d all along

Answer 19

\[a+2 \cdot (\frac{a-b^2}{2b})^2=a+2 \cdot \frac{a^2-2ab^2+b^4}{4b^2}\]
\[=a+\frac{a^2-2ab^2+b^4}{2b^2}=\frac{2ab^2+a^2-2ab^2+b^4}{2b^2}\]
\[=\frac{a^2+b^4}{2b^2}\]
wait our answer could have x and y in it ?
i didn't know that

Answer 20

I'm pretty certain the answer is d

Answer 21

x^2-y^2=a
(x+y)(x-y)=a and x-y=b so
(x+y)b=a
x+y=a/b
(x+y)^2=(a/b)^2
x^2+2xy+y^2=(a/b)^2
x^2+y^2-2xy+2xy=(a/b)^2-2xy
x^2+y^2=(a/b)^2-2xy

Answer 22

my answer is cooler than all of those

Answer 23

lol

Answer 24

yes it is actually

Answer 25

jahtoday, I like that. Simple and to the point

Answer 26

Thank you all!!! This great, I have spent hours on this

Answer 27

myininaya, if I could give you five medals, I would

Answer 28

lol

Answer 29

PLEASE!!! SOME ONE HELP!!! http://openstudy.com/groups/mathematics#/groups/mathematics/updates/4e499e390b8b8d00ebe47725

Answer 30

i love it! answer had a, b, x and y! lol

Answer 31

we had
\[(\frac{a}{b})^2=x^2+y^2+2xy\] and didn't know how to get rid of the 2xy part. turns out you just need to subtract! who knew?

Answer 32

lol, myininaya's answer is classier imo.

Answer 33

thanks joe :)