Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (25+x)-10=40
-
Equation x^2+4*x-21=0
-
Equation 2^x=10
-
Equation (x+1)^2=0
- 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)
-
Identical expressions
- f*(x)= four
- f multiply by (x) equally 4
- f multiply by (x) equally four
- f(x)=4
- fx=4
f*(x)=4 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 = 4/f
f*(x) = 4
Expand brackets in the left part
fx = 4
Divide both parts of the equation by f
x = 4 / (f)
We get the answer: x = 4/f
The solution of the parametric equation
Given the equation with a parameter:
$$f x = 4$$
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
$$- x - 4 = 0$$
its solution
$$x = -4$$
With
$$f = 0$$
the equation
$$-4 = 0$$
its solution
no solutions
$$f x = 4$$
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
$$- x - 4 = 0$$
its solution
$$x = -4$$
With
$$f = 0$$
the equation
$$-4 = 0$$
its solution
no solutions
The graph
Sum and product of roots
[src]
sum
4*re(f) 4*I*im(f) --------------- - --------------- 2 2 2 2 im (f) + re (f) im (f) + re (f)
$$\frac{4 \operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} - \frac{4 i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
=
4*re(f) 4*I*im(f) --------------- - --------------- 2 2 2 2 im (f) + re (f) im (f) + re (f)
$$\frac{4 \operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} - \frac{4 i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
product
4*re(f) 4*I*im(f) --------------- - --------------- 2 2 2 2 im (f) + re (f) im (f) + re (f)
$$\frac{4 \operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} - \frac{4 i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
=
4*(-I*im(f) + re(f))
--------------------
2 2
im (f) + re (f)
$$\frac{4 \left(\operatorname{re}{\left(f\right)} - i \operatorname{im}{\left(f\right)}\right)}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
4*(-i*im(f) + re(f))/(im(f)^2 + re(f)^2)
Rapid solution
[src]
4*re(f) 4*I*im(f)
x1 = --------------- - ---------------
2 2 2 2
im (f) + re (f) im (f) + re (f)
$$x_{1} = \frac{4 \operatorname{re}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}} - \frac{4 i \operatorname{im}{\left(f\right)}}{\left(\operatorname{re}{\left(f\right)}\right)^{2} + \left(\operatorname{im}{\left(f\right)}\right)^{2}}$$
x1 = 4*re(f)/(re(f)^2 + im(f)^2) - 4*i*im(f)/(re(f)^2 + im(f)^2)