Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 3x²-27=0
- Equation 9^x^2-x-5+6^x^2-x-4-180*4^x^2-X-7=0
- Equation x(y+1)2=243y
- Equation 3*x^4+9*x^2-30=0
- Express {x} in terms of y where:
- 10*x-1*y=10
- 15*x-17*y=19
- 9*x-8*y=6
- 15*x+15*y=16
-
Identical expressions
- x(y+ one) two =243y
- x(y plus 1)2 equally 243y
- x(y plus one) two equally 243y
- xy+12=243y
-
Similar expressions
- (15y+24)(3y-0.9)=0
- 1.243*((y^(0,142))/(x^(0,859)))=3,266*((y^(0,141))/(x^(0,858)))
- (243*y^2)^(1/3)=18+(81y)^(1/3)
- x(y-1)2=243y
x(y+1)2=243y 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 2 + 2*y
We get the answer: x = 243*y/(2*(1 + y))
x*(y+1)*2 = 243*y
Expand brackets in the left part
xy*2+1*2 = 243*y
Divide both parts of the equation by 2 + 2*y
x = 243*y / (2 + 2*y)
We get the answer: x = 243*y/(2*(1 + y))
The solution of the parametric equation
Given the equation with a parameter:
$$2 x \left(y + 1\right) = 243 y$$
Коэффициент при x равен
$$2 y + 2$$
then possible cases for y :
$$y < -1$$
$$y = -1$$
Consider all cases in more detail:
With
$$y < -1$$
the equation
$$486 - 2 x = 0$$
its solution
$$x = 243$$
With
$$y = -1$$
the equation
$$243 = 0$$
its solution
no solutions
$$2 x \left(y + 1\right) = 243 y$$
Коэффициент при x равен
$$2 y + 2$$
then possible cases for y :
$$y < -1$$
$$y = -1$$
Consider all cases in more detail:
With
$$y < -1$$
the equation
$$486 - 2 x = 0$$
its solution
$$x = 243$$
With
$$y = -1$$
the equation
$$243 = 0$$
its solution
no solutions
The graph
Rapid solution
[src]
/ y \ / y \
243*re|-----| 243*I*im|-----|
\1 + y/ \1 + y/
x1 = ------------- + ---------------
2 2
$$x_{1} = \frac{243 \operatorname{re}{\left(\frac{y}{y + 1}\right)}}{2} + \frac{243 i \operatorname{im}{\left(\frac{y}{y + 1}\right)}}{2}$$
x1 = 243*re(y/(y + 1))/2 + 243*i*im(y/(y + 1))/2
Sum and product of roots
[src]
sum
/ y \ / y \
243*re|-----| 243*I*im|-----|
\1 + y/ \1 + y/
------------- + ---------------
2 2
$$\frac{243 \operatorname{re}{\left(\frac{y}{y + 1}\right)}}{2} + \frac{243 i \operatorname{im}{\left(\frac{y}{y + 1}\right)}}{2}$$
=
/ y \ / y \
243*re|-----| 243*I*im|-----|
\1 + y/ \1 + y/
------------- + ---------------
2 2
$$\frac{243 \operatorname{re}{\left(\frac{y}{y + 1}\right)}}{2} + \frac{243 i \operatorname{im}{\left(\frac{y}{y + 1}\right)}}{2}$$
product
/ y \ / y \
243*re|-----| 243*I*im|-----|
\1 + y/ \1 + y/
------------- + ---------------
2 2
$$\frac{243 \operatorname{re}{\left(\frac{y}{y + 1}\right)}}{2} + \frac{243 i \operatorname{im}{\left(\frac{y}{y + 1}\right)}}{2}$$
=
/ y \ / y \
243*re|-----| 243*I*im|-----|
\1 + y/ \1 + y/
------------- + ---------------
2 2
$$\frac{243 \operatorname{re}{\left(\frac{y}{y + 1}\right)}}{2} + \frac{243 i \operatorname{im}{\left(\frac{y}{y + 1}\right)}}{2}$$
243*re(y/(1 + y))/2 + 243*i*im(y/(1 + y))/2