Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^4-4x^2+4=0
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Equation x^4=(3x-10)^2
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Equation (x+1)+(x+3)=5
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Equation 6x^2+x-7=0
- Express {x} in terms of y where:
- 12*x+5*y=7
- 9*x+9*y=7
- 17*x-10*y=16
- 15*x-2*y=-1
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Identical expressions
- five *x- four *y+z= one
- 5 multiply by x minus 4 multiply by y plus z equally 1
- five multiply by x minus four multiply by y plus z equally one
- 5x-4y+z=1
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Similar expressions
- 5*x-4*y-z=1
- 5*x+4*y+z=1
5*x-4*y+z=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the linear equation:
Looking for similar summands in the left part:
Move the summands with the other variables
from left part to right part, we given:
$$5 x - 4 y = 1 - z$$
Divide both parts of the equation by (-4*y + 5*x)/x
We get the answer: x = 1/5 - z/5 + 4*y/5
5*x-4*y+z = 1
Looking for similar summands in the left part:
z - 4*y + 5*x = 1
Move the summands with the other variables
from left part to right part, we given:
$$5 x - 4 y = 1 - z$$
Divide both parts of the equation by (-4*y + 5*x)/x
x = 1 - z / ((-4*y + 5*x)/x)
We get the answer: x = 1/5 - z/5 + 4*y/5
The graph
Rapid solution
[src]
1 re(z) 4*re(y) / im(z) 4*im(y)\
x1 = - - ----- + ------- + I*|- ----- + -------|
5 5 5 \ 5 5 /
$$x_{1} = i \left(\frac{4 \operatorname{im}{\left(y\right)}}{5} - \frac{\operatorname{im}{\left(z\right)}}{5}\right) + \frac{4 \operatorname{re}{\left(y\right)}}{5} - \frac{\operatorname{re}{\left(z\right)}}{5} + \frac{1}{5}$$
x1 = i*(4*im(y)/5 - im(z)/5) + 4*re(y)/5 - re(z)/5 + 1/5
Sum and product of roots
[src]
sum
1 re(z) 4*re(y) / im(z) 4*im(y)\ - - ----- + ------- + I*|- ----- + -------| 5 5 5 \ 5 5 /
$$i \left(\frac{4 \operatorname{im}{\left(y\right)}}{5} - \frac{\operatorname{im}{\left(z\right)}}{5}\right) + \frac{4 \operatorname{re}{\left(y\right)}}{5} - \frac{\operatorname{re}{\left(z\right)}}{5} + \frac{1}{5}$$
=
1 re(z) 4*re(y) / im(z) 4*im(y)\ - - ----- + ------- + I*|- ----- + -------| 5 5 5 \ 5 5 /
$$i \left(\frac{4 \operatorname{im}{\left(y\right)}}{5} - \frac{\operatorname{im}{\left(z\right)}}{5}\right) + \frac{4 \operatorname{re}{\left(y\right)}}{5} - \frac{\operatorname{re}{\left(z\right)}}{5} + \frac{1}{5}$$
product
1 re(z) 4*re(y) / im(z) 4*im(y)\ - - ----- + ------- + I*|- ----- + -------| 5 5 5 \ 5 5 /
$$i \left(\frac{4 \operatorname{im}{\left(y\right)}}{5} - \frac{\operatorname{im}{\left(z\right)}}{5}\right) + \frac{4 \operatorname{re}{\left(y\right)}}{5} - \frac{\operatorname{re}{\left(z\right)}}{5} + \frac{1}{5}$$
=
1 re(z) 4*re(y) I*(-im(z) + 4*im(y)) - - ----- + ------- + -------------------- 5 5 5 5
$$\frac{i \left(4 \operatorname{im}{\left(y\right)} - \operatorname{im}{\left(z\right)}\right)}{5} + \frac{4 \operatorname{re}{\left(y\right)}}{5} - \frac{\operatorname{re}{\left(z\right)}}{5} + \frac{1}{5}$$
1/5 - re(z)/5 + 4*re(y)/5 + i*(-im(z) + 4*im(y))/5