Maths help

[Tefal]

Can someone help me with this,

Find all solutions to the following equation in radians


2cos^2(x) - cos(x) -1 = 0


Can you show how you did it as i don't really get this.

Cheers.

 

[KaHn]

Do your own home work.........

KaHn

 

[Mr Jack]

It's a quadratic equation, substitute Y = cos(x), solve the equation:

2Y^2 - Y - 1 = 0

Then for each of your solutions for Y, list the values of x such that cos(x) = Y. I haven't solved it, but I'd expect you to get 4 solutions.

 

[Delvis]

It's a quadratic equation, substitute Y = cos(x), solve the equation:

2Y^2 - Y - 1 = 0

Then for each of your solutions for Y, list the values of x such that cos(x) = Y. I haven't solved it, but I'd expect you to get 4 solutions.

....Buh?

=/

 

[lord filbuster]

It's a quadratic equation, substitute Y = cos(x), solve the equation:

2Y^2 - Y - 1 = 0

Then for each of your solutions for Y, list the values of x such that cos(x) = Y. I haven't solved it, but I'd expect you to get 4 solutions.

Using this method, you can factorise to 2(y+1/2)(y-1) so, y=1, -1/2, since y=cos(x), the solutions are when cos(x)=1 or -1/2, so
cos(x)= 0°, 360°, 120°, 240° or in rads, 0, 2π, 2/3π, 4/3π

 

[Killa_ken]

2x^2 - 2x -1 = 0

solve for x so you get cos(x) = X then invese of cosine to get your X

 

[Mr Jack]

Using this method, you can factorise to 2(y+1/2)(y-1) so, y=1, -1/2, since y=cos(x), the solutions are when cos(x)=1 or -1/2, so
cos(x)= 0°, 360°, 120°, 240° or in rads, 0, 2π, 2/3π, 4/3π

0 and 2π are the same solution, so there are only 3 solutions in this case. Otherwise correct

 

[Rebelius]

they're not really the same solution, I'd write them both down to be on the safe side.

 

[Mr Jack]

they're not really the same solution, I'd write them both down to be on the safe side.

They're really the same solution. Exactly the same solution.

All your answers should be either in the range -π < x <= π or 0 <= x < 2π. Think about it, 2π away from where you start is back to the same point on the circle, as is 4π, 6π, 8π, -2π, -4π, and so on. If you're going to write 0 and 2π then you should be writing the infinite list of other solutions down. I'd expect you to lose marks for listing both, you certainly should as it shows a lack of understanding.

 

[ChrisD.]

they're not really the same solution, I'd write them both down to be on the safe side.

If it's an exam type question then you're right, or to be a smart **** you could prove how they are the same.

 

[Amleto]

they're not the same if you're on a riemann surface (iir the correct name for what I'm thinking of.)

 

[p4radox]

Using this method, you can factorise to 2(y+1/2)(y-1) so, y=1, -1/2, since y=cos(x), the solutions are when cos(x)=1 or -1/2, so
cos(x)= 0°, 360°, 120°, 240° or in rads, 0, 2π, 2/3π, 4/3π

This.