Solving 2 equation with 2 variables (hard)

Zetison

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:








But these solutions contains "cos". It is possible to rewrite the equations to the formula

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
Sorry mac, it is "79"