Question

xy=1
x^2+y^2 = 2
finf the values of x and y

Answer 1

it's a system of equations, solve the first one for one variable, then substitute it in to the second equation.

Answer 2

hi @cassie93 :)
there are multiple ways to do this, one of which can be using
\((x-y)^2 =... ? \\ (x+y)^2=...?\)
and get the values of x-y and x+y , then getting x,y will be very easy

Answer 3

or you could also start with what peter said, suit yourself :)

Answer 4

thnx....i get the idea...!! (x-y)(x+) ....thnx so much...:)

Answer 5

good!
also tell us what values of x, y you get , so that we can verify with our answers :)

Answer 6

because there are more than one pair of x,y values in the solution :)

Answer 7

i dnt knw hw to solve with 1/y^2....

Answer 8

you mean you got
1/y^2 + y^2 = 2
and you're stuck ?

Answer 9

yup...

Answer 10

find a common denominator

Answer 11

then multiply both sides by whatever that common denominator is

Answer 12

or if you want to avoid the 4th degree solving, you can assume
y^2 = a
1/a +a = 2

multiply 'a' throughout to get a easy quadratic :)

Answer 13

when you find values of 'a' , you can resubstitute back a = y^2 to get values of y :)

Answer 14

let us know if you have difficulty finding 'a' values

Answer 15

i dnt undrstand about the y^2 = a
1/a +a = 2

Answer 16

we had 1/y^2 + y^2 = 2
right ?
thats an equation in y^2
instead of working with y^2, i can take a new variable (here i took 'a') to simplify solving it
i just replaced every y^2 by 'a'
this is called substitution
hence i get
1/a + a = 2

Answer 17

^what he said

Answer 18

so, there is two values of 'a'..? i got a=0.4142 and a=-2.4142

Answer 19

is tht correct?

Answer 20

how did you get those ?

did you do this ?
1/a + a = 2
1 + a^2 = 2a
a^2 -2a +1 =0
??

Answer 21

oh, i got a=1

Answer 22

that is indeed correct! :)
y^2 = 1
then values of y are .. ?

Answer 23

so, substitute y^2=1 into 1/y^2+y^2=2....?

Answer 24

you can actually find the values of y from y^2 =1

Answer 25

hint : *cough* take square root on both sides *cough*

Answer 26

remember that a negative times a negative equals a positive...

Answer 27

*gives hartnn water*

Answer 28

so, the values of x=1,-1 y=1,-1 ....??

Answer 29

yes!

Answer 30

exactly right

Answer 31

when y=1, you get x=1, right ?
so actually write those as
(1,1) and (-1,-1)

Answer 32

TTHHHHAAAAANNNNKKKK UUUUUU PEOPLE......!!! :) U GUYS AWESOME..!!

Answer 33

you're awesome too! :D
welcome ^_^

Answer 34

you're the awesome one, we just guided you to the answer

Answer 35

any other questions?

Answer 36

thts it so far..:) thnx by the way...:)

Answer 37

you're welcome

Answer 38

so where are you from? (the messages aren't working right now)

Answer 39

Philippine :)

Answer 40

do you live there now?

Answer 41

yup...y?

Answer 42

I am an American living in Beijing, China

Answer 43

well yes, sort of. my dad works here. I am a senior in high school, so I'm not in college yet.

Answer 44

you are in college?

Answer 45

yup, 1st year.. all about refrshing the high school subjects.. and my weakness is in math..

Answer 46

haha, my strength is math, so I can help you

Answer 47

cool... now i knw where to find help...:)

Answer 48

you seem like an interesting person

Answer 49

#replied u in inbox :)

Answer 50

Thank you XD
(inbox doesn't work very well right now, you have to refresh the page to see if messages have been sent.)

Answer 51

LOL...ok..just talk here then...:)

Answer 52

ok,
what's your favorite subject?

Answer 53

Bio... (i'm taking Biological Engineering) :)

Answer 54

oh wow, you're smart :)
biological engineering on the small scale like DNA modification or other stuff like the use of biology in industry?

Answer 55

yup..exactly...(but not tht smart)... ^_^

Answer 56

I'm sure you're just being humble.

Answer 57

my nature. ^_^ wht about u? any plan for college?

Answer 58

I plan to go back to the US. I plan on studying engineering, either mechanical or petroleum.

Answer 59

cool...tht suits u... u'r smart, u can take any course u wnt..:) maybe u'll end up in MIT?

Answer 60

haha no, my grades aren't nearly good enough for that. I'm smart but lazy.

Answer 61

haha... u'll do fine...

Answer 62

and on top of that, i'm white. I know only two people who got into MIT, and they were both hispanic (so they had an advantage with admissions) and had better grades than I do.

Answer 63

hmm... anyway, u'll succeed someday.. :) it's a guarantee.. just embrace ur gift wisely... ^_^

Answer 64

wnt to ask smthing, is X^3 = 1, then X= +-1 ?

Answer 65

if x^3 = 1, x is 1, (sqrt(3)/2 + 0.5i) or (sqrt(3)/2 - 0.5i)

Answer 66

ok...^_^thnx... i got to go... i got Bio quiz 2morrow, need to study... ^_^ nice to meet u Peter... stay connected... ^_^

Answer 67

bye

Answer 68

I sent you a message

Answer 69

wow you 2 had pretty good convo. :)
thank god notification system also isn't working :P else i would've got notifications like every minute :O

Answer 70

if the notification system was working, the message system would be working too and we would have this convo there

Answer 71

oh, oops, I got the cube root of one wrong. it's actually 1, -0.5+0.5sqrt(3)i, and -0.5-0.5sqrt(3)i