# Hey everyone, I'm Wu =) Nice to meet you

• Jul 31st 2012, 03:48 AM
moneyloser12345
Hey everyone, I'm Wu =) Nice to meet you
Currently studying math, sorry if my english is bad.

I am Wu Zhong Lan.
I am 18 years old =)

I am puzzled with some questions.

Questions:
3 equations xy = 1 x^2 + y^2 = 1 x^2 + y^2 = 4

In surd form, show the 4 intersections of the last graphs with the first.
I am puzzled to where to start :S

Thank you =)
• Jul 31st 2012, 06:12 AM
HallsofIvy
Re: Hey everyone, I'm Wu =) Nice to meet you
Well, an obvious start would be to draw the graphs since that is what is asked. Or you could solve as pairs of equations. The graphs of $xy= 1$ and $x^2+ y^2= 1$ intersect when both equations are satisfied. From xy= 1, y= 1/x so the second equation is $x^2+ (\frac{1}{x})^2= x^2+ \frac{1}{x^2}= 1$. Multiplying both sides of that by $x^2$ gives $x^4+ 1= x^2$. Let $u= x^2$ and that becomes $u^2+ 1= u$ or $u^2- u+ 1= 0$. Can you solve that quadratic equation?

The graphs of $xy= 1$ and $x^2+ y^2= 4$ intersect where both equations are satisfied. Do the same as above.
• Jul 31st 2012, 02:59 PM
moneyloser12345
Re: Hey everyone, I'm Wu =) Nice to meet you
Ahhhh yes yes, I see. thank you a lot! =)