Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation z^2-4*z+5=0
-
Equation (25+x)-10=40
-
Equation x^2+4*x-21=0
-
Equation 2^x=10
- Express {x} in terms of y where:
- 11*x+3*y=-16
- -2*x+13*y=-6
- 20*x-3*y=3
- 18*x-7*y=-4
- Derivative of:
- f*(x)
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Identical expressions
- f*(x)=+oo
- f multiply by (x) equally plus oo
- f(x)=+oo
- fx=+oo
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Similar expressions
- f*(x)=-oo
f*(x)=+oo equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the linear equation:
Expand brackets in the left part
Divide both parts of the equation by f
We get the answer: x = oo/f
f*(x) = +oo
Expand brackets in the left part
fx = +oo
Divide both parts of the equation by f
x = oo / (f)
We get the answer: x = oo/f
The solution of the parametric equation
Given the equation with a parameter:
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
$$-\infty = 0$$
its solution
no solutions
With
$$f = 0$$
the equation
$$-\infty = 0$$
its solution
no solutions
False
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
$$-\infty = 0$$
its solution
no solutions
With
$$f = 0$$
the equation
$$-\infty = 0$$
its solution
no solutions
The graph
Rapid solution
[src]
oo*re(f) oo*I*im(f)
x1 = --------------- - ---------------
2 2 2 2
im (f) + re (f) im (f) + re (f)
$$x_{1} = \frac{\infty \operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} - \frac{\infty i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
x1 = oo*re(f)/(re(f)^2 + im(f)^2) - oo*i*im(f)/(re(f)^2 + im(f)^2)
Sum and product of roots
[src]
sum
oo*re(f) oo*I*im(f) --------------- - --------------- 2 2 2 2 im (f) + re (f) im (f) + re (f)
$$\frac{\infty \operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} - \frac{\infty i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
=
oo*re(f) oo*I*im(f) --------------- - --------------- 2 2 2 2 im (f) + re (f) im (f) + re (f)
$$\frac{\infty \operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} - \frac{\infty i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
product
oo*re(f) oo*I*im(f) --------------- - --------------- 2 2 2 2 im (f) + re (f) im (f) + re (f)
$$\frac{\infty \operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} - \frac{\infty i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
=
oo*(-I*im(f) + re(f))
---------------------
2 2
im (f) + re (f)
$$\frac{\infty \left(\operatorname{re}{\left(f\right)} - i \operatorname{im}{\left(f\right)}\right)}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
oo*(-i*im(f) + re(f))/(im(f)^2 + re(f)^2)