f*(x)=2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the linear equation:
f*(x) = 2
Expand brackets in the left part
fx = 2
Divide both parts of the equation by f
x = 2 / (f)
We get the answer: x = 2/f
The solution of the parametric equation
Given the equation with a parameter:
$$f x = 2$$
Коэффициент при x равен
$$f$$
then possible cases for f :
$$f < 0$$
$$f = 0$$
Consider all cases in more detail:
With
$$f < 0$$
the equation
$$- x - 2 = 0$$
its solution
$$x = -2$$
With
$$f = 0$$
the equation
$$-2 = 0$$
its solution
no solutions
Sum and product of roots
[src]
2*re(f) 2*I*im(f)
--------------- - ---------------
2 2 2 2
im (f) + re (f) im (f) + re (f)
$$\frac{2 \operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} - \frac{2 i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
2*re(f) 2*I*im(f)
--------------- - ---------------
2 2 2 2
im (f) + re (f) im (f) + re (f)
$$\frac{2 \operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} - \frac{2 i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
2*re(f) 2*I*im(f)
--------------- - ---------------
2 2 2 2
im (f) + re (f) im (f) + re (f)
$$\frac{2 \operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} - \frac{2 i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
2*(-I*im(f) + re(f))
--------------------
2 2
im (f) + re (f)
$$\frac{2 \left(\operatorname{re}{\left(f\right)} - i \operatorname{im}{\left(f\right)}\right)}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
2*(-i*im(f) + re(f))/(im(f)^2 + re(f)^2)
2*re(f) 2*I*im(f)
x1 = --------------- - ---------------
2 2 2 2
im (f) + re (f) im (f) + re (f)
$$x_{1} = \frac{2 \operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} - \frac{2 i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
x1 = 2*re(f)/(re(f)^2 + im(f)^2) - 2*i*im(f)/(re(f)^2 + im(f)^2)