Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2005-12-16 13:05:17

sirsosay
Member

Offline

Finding the intersection of two functions.

xy=2 and x²-y²=3

I got y by itself then I got...

2/x = ±√(x²-3)

I'm stuck at 4 = x^4-3x²

Last edited by sirsosay (2005-12-16 13:05:40)

#2 2005-12-16 14:00:55

MajikWaffle
Member

Offline

Re: Finding the intersection of two functions.

x^4 - 3x^2 - 4 = 0

(x^2 - 4)(x^2 +1) = 0

x^2 - 4 = 0                   x^2 + 1 = 0
x^2 = 4                        x^2 = -1
x = +- 2                       x = +- i

Last edited by MajikWaffle (2005-12-16 14:01:17)

#3 2005-12-16 14:03:59

John E. Franklin
Star Member

Offline

Re: Finding the intersection of two functions.

I get (-2,-1) and (2,1) by graphing a sketch.

And I guess majicWaffle is right,
also (i, -2i) and (-i, 2i), whatever these complex thingys mean, I don't remember.

Last edited by John E. Franklin (2005-12-16 14:28:01)

Imagine for a moment that even an earthworm may possess a love of self and a love of others.

sirsosay
Member

Offline

Thank you!

#5 2005-12-16 15:08:41

Ricky
Moderator

Offline

Re: Finding the intersection of two functions.

"also (i, -2i) and (-i, 2i), whatever these complex thingys mean, I don't remember."

Every nth degree equation has n solutions.  Some solutions may be double roots (i.e. (x-1)(x-1) = 0).  The graph may only pass through the x-axis (where y = 0, which would be a solutions) less than n times.  When this occurs, you get an imaginary solution, which is what i is.

Last edited by Ricky (2005-12-16 15:08:54)

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."