Mister Exam
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How to use it?
- Equation:
-
Equation 16x-3=8x-43
-
Equation x^2-3x+1=0
-
Equation x^2-5*x-5=0
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Equation x/9+x=-3
- Express {x} in terms of y where:
- 1*x+6*y=-6
- -5*x-2*y=9
- 1*x+11*y=-3
- 17*x-19*y=-12
-
Identical expressions
- (z9) five ⋅(z four) eight (z4)4⋅(z4) fifteen = seven .
- (z9)5⋅(z4)8(z4)4⋅(z4)15 equally 7.
- (z9) five ⋅(z four) eight (z4)4⋅(z4) fifteen equally seven .
- z95⋅z48z44⋅z415=7.
(z9)5⋅(z4)8(z4)4⋅(z4)15=7. equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
z9*5*z4*8*z4*4*z4*15 = 7
$$15 z_{4} \cdot 4 z_{4} \cdot 8 z_{4} \cdot 5 z_{9} = 7$$
Detail solution
Given the linear equation:
Expand brackets in the left part
Divide both parts of the equation by 2400*z4^3
We get the answer: z9 = 7/(2400*z4^3)
(z9)*5*(z4)*8*(z4)*4*(z4)*15 = 7
Expand brackets in the left part
z9*5z4*8z4*4z4*15 = 7
Divide both parts of the equation by 2400*z4^3
z9 = 7 / (2400*z4^3)
We get the answer: z9 = 7/(2400*z4^3)
The solution of the parametric equation
Given the equation with a parameter:
$$2400 z_{4}^{3} z_{9} = 7$$
Коэффициент при z9 равен
$$2400 z_{4}^{3}$$
then possible cases for z4 :
$$z_{4} < 0$$
$$z_{4} = 0$$
Consider all cases in more detail:
With
$$z_{4} < 0$$
the equation
$$- 2400 z_{9} - 7 = 0$$
its solution
$$z_{9} = - \frac{7}{2400}$$
With
$$z_{4} = 0$$
the equation
$$-7 = 0$$
its solution
no solutions
$$2400 z_{4}^{3} z_{9} = 7$$
Коэффициент при z9 равен
$$2400 z_{4}^{3}$$
then possible cases for z4 :
$$z_{4} < 0$$
$$z_{4} = 0$$
Consider all cases in more detail:
With
$$z_{4} < 0$$
the equation
$$- 2400 z_{9} - 7 = 0$$
its solution
$$z_{9} = - \frac{7}{2400}$$
With
$$z_{4} = 0$$
the equation
$$-7 = 0$$
its solution
no solutions
The graph
Rapid solution
[src]
/ 3 2 \ 3 2
| 7*im (z4) 7*re (z4)*im(z4) | 7*re (z4) 7*im (z4)*re(z4)
z91 = I*|------------------------- - ------------------------| + ------------------------- - ------------------------
| 3 3| 3 3
| / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \
\2400*\im (z4) + re (z4)/ 800*\im (z4) + re (z4)/ / 2400*\im (z4) + re (z4)/ 800*\im (z4) + re (z4)/
$$z_{91} = i \left(- \frac{7 \left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} \operatorname{im}{\left(z_{4}\right)}}{800 \left(\left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} + \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right)^{3}} + \frac{7 \left(\operatorname{im}{\left(z_{4}\right)}\right)^{3}}{2400 \left(\left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} + \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right)^{3}}\right) + \frac{7 \left(\operatorname{re}{\left(z_{4}\right)}\right)^{3}}{2400 \left(\left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} + \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right)^{3}} - \frac{7 \operatorname{re}{\left(z_{4}\right)} \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}}{800 \left(\left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} + \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right)^{3}}$$
z91 = i*(-7*re(z4)^2*im(z4)/(800*(re(z4)^2 + im(z4)^2)^3) + 7*im(z4)^3/(2400*(re(z4)^2 + im(z4)^2)^3)) + 7*re(z4)^3/(2400*(re(z4)^2 + im(z4)^2)^3) - 7*re(z4)*im(z4)^2/(800*(re(z4)^2 + im(z4)^2)^3)
Sum and product of roots
[src]
sum
/ 3 2 \ 3 2 | 7*im (z4) 7*re (z4)*im(z4) | 7*re (z4) 7*im (z4)*re(z4) I*|------------------------- - ------------------------| + ------------------------- - ------------------------ | 3 3| 3 3 | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ \2400*\im (z4) + re (z4)/ 800*\im (z4) + re (z4)/ / 2400*\im (z4) + re (z4)/ 800*\im (z4) + re (z4)/
$$i \left(- \frac{7 \left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} \operatorname{im}{\left(z_{4}\right)}}{800 \left(\left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} + \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right)^{3}} + \frac{7 \left(\operatorname{im}{\left(z_{4}\right)}\right)^{3}}{2400 \left(\left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} + \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right)^{3}}\right) + \frac{7 \left(\operatorname{re}{\left(z_{4}\right)}\right)^{3}}{2400 \left(\left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} + \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right)^{3}} - \frac{7 \operatorname{re}{\left(z_{4}\right)} \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}}{800 \left(\left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} + \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right)^{3}}$$
=
/ 3 2 \ 3 2 | 7*im (z4) 7*re (z4)*im(z4) | 7*re (z4) 7*im (z4)*re(z4) I*|------------------------- - ------------------------| + ------------------------- - ------------------------ | 3 3| 3 3 | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ \2400*\im (z4) + re (z4)/ 800*\im (z4) + re (z4)/ / 2400*\im (z4) + re (z4)/ 800*\im (z4) + re (z4)/
$$i \left(- \frac{7 \left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} \operatorname{im}{\left(z_{4}\right)}}{800 \left(\left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} + \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right)^{3}} + \frac{7 \left(\operatorname{im}{\left(z_{4}\right)}\right)^{3}}{2400 \left(\left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} + \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right)^{3}}\right) + \frac{7 \left(\operatorname{re}{\left(z_{4}\right)}\right)^{3}}{2400 \left(\left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} + \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right)^{3}} - \frac{7 \operatorname{re}{\left(z_{4}\right)} \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}}{800 \left(\left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} + \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right)^{3}}$$
product
/ 3 2 \ 3 2 | 7*im (z4) 7*re (z4)*im(z4) | 7*re (z4) 7*im (z4)*re(z4) I*|------------------------- - ------------------------| + ------------------------- - ------------------------ | 3 3| 3 3 | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ \2400*\im (z4) + re (z4)/ 800*\im (z4) + re (z4)/ / 2400*\im (z4) + re (z4)/ 800*\im (z4) + re (z4)/
$$i \left(- \frac{7 \left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} \operatorname{im}{\left(z_{4}\right)}}{800 \left(\left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} + \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right)^{3}} + \frac{7 \left(\operatorname{im}{\left(z_{4}\right)}\right)^{3}}{2400 \left(\left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} + \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right)^{3}}\right) + \frac{7 \left(\operatorname{re}{\left(z_{4}\right)}\right)^{3}}{2400 \left(\left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} + \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right)^{3}} - \frac{7 \operatorname{re}{\left(z_{4}\right)} \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}}{800 \left(\left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} + \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right)^{3}}$$
=
/ 3 2 / 2 2 \ \
7*\re (z4) - 3*im (z4)*re(z4) + I*\im (z4) - 3*re (z4)/*im(z4)/
---------------------------------------------------------------
3
/ 2 2 \
2400*\im (z4) + re (z4)/
$$\frac{7 \left(i \left(- 3 \left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} + \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right) \operatorname{im}{\left(z_{4}\right)} + \left(\operatorname{re}{\left(z_{4}\right)}\right)^{3} - 3 \operatorname{re}{\left(z_{4}\right)} \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right)}{2400 \left(\left(\operatorname{re}{\left(z_{4}\right)}\right)^{2} + \left(\operatorname{im}{\left(z_{4}\right)}\right)^{2}\right)^{3}}$$
7*(re(z4)^3 - 3*im(z4)^2*re(z4) + i*(im(z4)^2 - 3*re(z4)^2)*im(z4))/(2400*(im(z4)^2 + re(z4)^2)^3)