Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^4-4x^2+4=0
-
Equation x^4=(3x-10)^2
-
Equation (x+1)+(x+3)=5
-
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
- x4-17x2+ sixteen = zero
- x4 minus 17x2 plus 16 equally 0
- x4 minus 17x2 plus sixteen equally zero
- x4-17x2+16=O
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Similar expressions
- x4-17x2-16=0
- x4+17x2+16=0
x4-17x2+16=0 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 free summands (without x4)
from left part to right part, we given:
$$- 17 x_{2} + x_{4} = -16$$
Move the summands with the other variables
from left part to right part, we given:
$$\left(-17\right) x_{2} = - x_{4} - 16$$
Divide both parts of the equation by -17*x2/x4
We get the answer: x4 = -16 + 17*x2
x4-17*x2+16 = 0
Looking for similar summands in the left part:
16 + x4 - 17*x2 = 0
Move free summands (without x4)
from left part to right part, we given:
$$- 17 x_{2} + x_{4} = -16$$
Move the summands with the other variables
from left part to right part, we given:
$$\left(-17\right) x_{2} = - x_{4} - 16$$
Divide both parts of the equation by -17*x2/x4
x4 = -16 - x4 / (-17*x2/x4)
We get the answer: x4 = -16 + 17*x2
The graph
Rapid solution
[src]
x41 = -16 + 17*re(x2) + 17*I*im(x2)
$$x_{41} = 17 \operatorname{re}{\left(x_{2}\right)} + 17 i \operatorname{im}{\left(x_{2}\right)} - 16$$
x41 = 17*re(x2) + 17*i*im(x2) - 16
Sum and product of roots
[src]
sum
-16 + 17*re(x2) + 17*I*im(x2)
$$17 \operatorname{re}{\left(x_{2}\right)} + 17 i \operatorname{im}{\left(x_{2}\right)} - 16$$
=
-16 + 17*re(x2) + 17*I*im(x2)
$$17 \operatorname{re}{\left(x_{2}\right)} + 17 i \operatorname{im}{\left(x_{2}\right)} - 16$$
product
-16 + 17*re(x2) + 17*I*im(x2)
$$17 \operatorname{re}{\left(x_{2}\right)} + 17 i \operatorname{im}{\left(x_{2}\right)} - 16$$
=
-16 + 17*re(x2) + 17*I*im(x2)
$$17 \operatorname{re}{\left(x_{2}\right)} + 17 i \operatorname{im}{\left(x_{2}\right)} - 16$$
-16 + 17*re(x2) + 17*i*im(x2)