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

1. ## 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 =)

2. ## 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 $\displaystyle xy= 1$ and $\displaystyle x^2+ y^2= 1$ intersect when both equations are satisfied. From xy= 1, y= 1/x so the second equation is $\displaystyle x^2+ (\frac{1}{x})^2= x^2+ \frac{1}{x^2}= 1$. Multiplying both sides of that by $\displaystyle x^2$ gives $\displaystyle x^4+ 1= x^2$. Let $\displaystyle u= x^2$ and that becomes $\displaystyle u^2+ 1= u$ or $\displaystyle u^2- u+ 1= 0$. Can you solve that quadratic equation?

The graphs of $\displaystyle xy= 1$ and $\displaystyle x^2+ y^2= 4$ intersect where both equations are satisfied. Do the same as above.

3. ## Re: Hey everyone, I'm Wu =) Nice to meet you

Ahhhh yes yes, I see. thank you a lot! =)