Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 10/(x+6)=1
-
Equation -2*(-2-y)-y-2=0
-
Equation 2*x^2+18*x=0
- Equation 2ax=6
- Express {x} in terms of y where:
- -4*x-9*y=12
- -2*x+15*y=9
- -1*x+11*y=3
- -5*x+15*y=6
- Integral of d{x}:
- 2ax
- Derivative of:
- 2ax
-
Identical expressions
- 2ax= six
- 2ax equally 6
- 2ax equally six
-
Similar expressions
- 2*a-x*a^2+(x^3)/6-3*a*x^2-12*z*a^2+12*a^3-(z^2)/6-2*a*x/3+2*(a^2)/3=0
- x^2+2*a*x+6a=0
2ax=6 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the linear equation:
Divide both parts of the equation by 2*a
We get the answer: x = 3/a
2*a*x = 6
Divide both parts of the equation by 2*a
x = 6 / (2*a)
We get the answer: x = 3/a
The solution of the parametric equation
Given the equation with a parameter:
$$2 a x = 6$$
Коэффициент при x равен
$$2 a$$
then possible cases for a :
$$a < 0$$
$$a = 0$$
Consider all cases in more detail:
With
$$a < 0$$
the equation
$$- 2 x - 6 = 0$$
its solution
$$x = -3$$
With
$$a = 0$$
the equation
$$-6 = 0$$
its solution
no solutions
$$2 a x = 6$$
Коэффициент при x равен
$$2 a$$
then possible cases for a :
$$a < 0$$
$$a = 0$$
Consider all cases in more detail:
With
$$a < 0$$
the equation
$$- 2 x - 6 = 0$$
its solution
$$x = -3$$
With
$$a = 0$$
the equation
$$-6 = 0$$
its solution
no solutions
The graph
Rapid solution
[src]
3*re(a) 3*I*im(a)
x1 = --------------- - ---------------
2 2 2 2
im (a) + re (a) im (a) + re (a)
$$x_{1} = \frac{3 \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{3 i \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
x1 = 3*re(a)/(re(a)^2 + im(a)^2) - 3*i*im(a)/(re(a)^2 + im(a)^2)
Sum and product of roots
[src]
sum
3*re(a) 3*I*im(a) --------------- - --------------- 2 2 2 2 im (a) + re (a) im (a) + re (a)
$$\frac{3 \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{3 i \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
=
3*re(a) 3*I*im(a) --------------- - --------------- 2 2 2 2 im (a) + re (a) im (a) + re (a)
$$\frac{3 \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{3 i \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
product
3*re(a) 3*I*im(a) --------------- - --------------- 2 2 2 2 im (a) + re (a) im (a) + re (a)
$$\frac{3 \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{3 i \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
=
3*(-I*im(a) + re(a))
--------------------
2 2
im (a) + re (a)
$$\frac{3 \left(\operatorname{re}{\left(a\right)} - i \operatorname{im}{\left(a\right)}\right)}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
3*(-i*im(a) + re(a))/(im(a)^2 + re(a)^2)