Solving 2 equation with 2 variables (hard)

[Zetison]

[PLAIN]http://folk.ntnu.no/jonvegar/images/math.gif

I really need some help here (no program is allowed )

 

[Pengwuino]

What work have you done on the problem so far?

 

[HallsofIvy]

I'm not sure why you would consider that "hard". You can solve the second equation for x as a quadratic function of y. Putting that into the first equation gives a cubic equation for y.

 

[Zetison]

The problem is to find exact values, not estimatet values. Therefore: do not use any programs...

 

[Gib Z]

Indeed. Do you have any strategies to find a root? There are many you can try. Once you find one, you can divide and just solve a quadratic.

 

[Zetison]

Here is what I have done so far:

[PLAIN]http://folk.ntnu.no/jonvegar/images/1.gif
[PLAIN]http://folk.ntnu.no/jonvegar/images/2.gif
[PLAIN]http://folk.ntnu.no/jonvegar/images/3.gif
[PLAIN]http://folk.ntnu.no/jonvegar/images/4.gif
[PLAIN]http://folk.ntnu.no/jonvegar/images/5.gif
[PLAIN]http://folk.ntnu.no/jonvegar/images/6.gif

But these solutions contains "cos". It is possible to rewrite the equations to the formula
[PLAIN]http://folk.ntnu.no/jonvegar/images/8.gif
and then find solutions without any trigonometrical components.

That is my problem...

 

[Gib Z]

Would have been a simpler computation for the program to have changed the x into 1/y rather than the other way around, small numbers to deal with overall. Were you expected to solve this cubic analytically and it's roots actually looked like that?

 

[Zetison]

Yes. It does not matter how you start. You will get the same solutions with the same trigonometrical components. Plz help me find solutions without any trigonometrical components.

 

[Count Iblis]

There is a typo in the problem: "79" should be "78".

 

[Gib Z]

Is it just because the answer drops our nicely if that is the case, or do you somehow know it as a fact :S ?

 

[Zetison]

I just somehow know it is a fact

There is a typo in the problem: "79" should be "78".

Sorry mac, it is "79"