How to solve Simultaneous Quadratic Equations?

I have to solve two quadratic equations simultaneously as follows:

a1*tan^2(x)+b1*tan(x)+c1=0

a2*tan^2(r*x)+b2*tan(r*x)+c2=0

Here, a1, a2, b1, b2, c1, c2, r are known quantities.

I have to find out the value of x.

Thanks in advance.

Answer 1

[John D'Errico]

These are not quadratic equations. The mere possession of a square in there does not make it quadratic. The possession of tan(x) does makes it nonlinear.

Use fsolve or vpasolve.

Oh. And learn how to write the square of a function in MATLAB. tan^2(x) is not valid syntax. tan(x)^2 or tan(x).^2 is valid syntax.

[Antra Saxena]

Thank You.

Answer 2

[Torsten]

For the first equation, substitute y = tan(x) and solve the quadratic equation in y.

For the second equation, substitute z = tan(r*x) and solve the quadratic equation in z.

If atan(y) = 1/r*atan(z), the system from above has a solution: x = atan(y) ( = 1/r*atan(z)).

Best wishes

Torsten.

[Antra Saxena]

Thanks for the answer.

But as you mentioned, If atan(y) = 1/r*atan(z), then solution is x = atan(y) ( = 1/r*atan(z)), but it is not satisfying.

[Torsten]

Then there is no solution.

[Antra Saxena]

Ok. Thanks