Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 31+25x+2x^2=7x-9
-
Equation sin(x)=sqrt2/2
- Equation Cx-1^x*(x-1)=30
- Equation 3y^2+y-24/9-y^2=-2
- Express {x} in terms of y where:
- 9*x+18*y=6
- 15*x-15*y=16
- (x^2+y^2-1)^3+x^2*y^3=0
- 4*x-16*y=6
- Sum of series:
-
30
- Derivative of:
- 30
- 30
-
Identical expressions
- Cx- one ^x*(x- one)= thirty
- Cx minus 1 to the power of x multiply by (x minus 1) equally 30
- Cx minus one to the power of x multiply by (x minus one) equally thirty
- Cx-1x*(x-1)=30
- Cx-1x*x-1=30
- Cx-1^x(x-1)=30
- Cx-1x(x-1)=30
- Cx-1xx-1=30
- Cx-1^xx-1=30
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Similar expressions
- Cx-1^x*(x+1)=30
- Cx+1^x*(x-1)=30
Cx-1^x*(x-1)=30 equation
The teacher will be very surprised to see your correct solution 😉
The solution
The solution of the parametric equation
Given the equation with a parameter:
$$c x - x + 1 = 30$$
Коэффициент при x равен
$$c - 1$$
then possible cases for c :
$$c < 1$$
$$c = 1$$
Consider all cases in more detail:
With
$$c < 1$$
the equation
$$- x - 29 = 0$$
its solution
$$x = -29$$
With
$$c = 1$$
the equation
$$-29 = 0$$
its solution
no solutions
$$c x - x + 1 = 30$$
Коэффициент при x равен
$$c - 1$$
then possible cases for c :
$$c < 1$$
$$c = 1$$
Consider all cases in more detail:
With
$$c < 1$$
the equation
$$- x - 29 = 0$$
its solution
$$x = -29$$
With
$$c = 1$$
the equation
$$-29 = 0$$
its solution
no solutions
The graph
Rapid solution
[src]
29*(-1 + re(c)) 29*I*im(c)
x1 = ---------------------- - ----------------------
2 2 2 2
(-1 + re(c)) + im (c) (-1 + re(c)) + im (c)
$$x_{1} = \frac{29 \left(\operatorname{re}{\left(c\right)} - 1\right)}{\left(\operatorname{re}{\left(c\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} - \frac{29 i \operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(c\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}}$$
x1 = 29*(re(c) - 1)/((re(c) - 1)^2 + im(c)^2) - 29*i*im(c)/((re(c) - 1)^2 + im(c)^2)
Sum and product of roots
[src]
sum
29*(-1 + re(c)) 29*I*im(c)
---------------------- - ----------------------
2 2 2 2
(-1 + re(c)) + im (c) (-1 + re(c)) + im (c)
$$\frac{29 \left(\operatorname{re}{\left(c\right)} - 1\right)}{\left(\operatorname{re}{\left(c\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} - \frac{29 i \operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(c\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}}$$
=
29*(-1 + re(c)) 29*I*im(c)
---------------------- - ----------------------
2 2 2 2
(-1 + re(c)) + im (c) (-1 + re(c)) + im (c)
$$\frac{29 \left(\operatorname{re}{\left(c\right)} - 1\right)}{\left(\operatorname{re}{\left(c\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} - \frac{29 i \operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(c\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}}$$
product
29*(-1 + re(c)) 29*I*im(c)
---------------------- - ----------------------
2 2 2 2
(-1 + re(c)) + im (c) (-1 + re(c)) + im (c)
$$\frac{29 \left(\operatorname{re}{\left(c\right)} - 1\right)}{\left(\operatorname{re}{\left(c\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} - \frac{29 i \operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(c\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}}$$
=
29*(-1 - I*im(c) + re(c))
-------------------------
2 2
(-1 + re(c)) + im (c)
$$\frac{29 \left(\operatorname{re}{\left(c\right)} - i \operatorname{im}{\left(c\right)} - 1\right)}{\left(\operatorname{re}{\left(c\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}}$$
29*(-1 - i*im(c) + re(c))/((-1 + re(c))^2 + im(c)^2)