Mister Exam

Diğer hesaplayıcılar

x1^4-x2^4 denklem

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Sayısal çözüm:

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Çözüm

You have entered [src]
  4     4    
x1  - x2  = 0
$$x_{1}^{4} - x_{2}^{4} = 0$$
The graph
Sum and product of roots [src]
sum
-re(x1) - I*im(x1) + I*im(x1) + re(x1) + -I*re(x1) + im(x1) + -im(x1) + I*re(x1)
$$\left(i \operatorname{re}{\left(x_{1}\right)} - \operatorname{im}{\left(x_{1}\right)}\right) + \left(\left(- i \operatorname{re}{\left(x_{1}\right)} + \operatorname{im}{\left(x_{1}\right)}\right) + \left(\left(- \operatorname{re}{\left(x_{1}\right)} - i \operatorname{im}{\left(x_{1}\right)}\right) + \left(\operatorname{re}{\left(x_{1}\right)} + i \operatorname{im}{\left(x_{1}\right)}\right)\right)\right)$$
=
0
$$0$$
product
(-re(x1) - I*im(x1))*(I*im(x1) + re(x1))*(-I*re(x1) + im(x1))*(-im(x1) + I*re(x1))
$$\left(- \operatorname{re}{\left(x_{1}\right)} - i \operatorname{im}{\left(x_{1}\right)}\right) \left(\operatorname{re}{\left(x_{1}\right)} + i \operatorname{im}{\left(x_{1}\right)}\right) \left(- i \operatorname{re}{\left(x_{1}\right)} + \operatorname{im}{\left(x_{1}\right)}\right) \left(i \operatorname{re}{\left(x_{1}\right)} - \operatorname{im}{\left(x_{1}\right)}\right)$$
=
                    2                    2
(-im(x1) + I*re(x1)) *(I*im(x1) + re(x1)) 
$$\left(i \operatorname{re}{\left(x_{1}\right)} - \operatorname{im}{\left(x_{1}\right)}\right)^{2} \left(\operatorname{re}{\left(x_{1}\right)} + i \operatorname{im}{\left(x_{1}\right)}\right)^{2}$$
(-im(x1) + i*re(x1))^2*(i*im(x1) + re(x1))^2
Rapid solution [src]
x21 = -re(x1) - I*im(x1)
$$x_{21} = - \operatorname{re}{\left(x_{1}\right)} - i \operatorname{im}{\left(x_{1}\right)}$$
x22 = I*im(x1) + re(x1)
$$x_{22} = \operatorname{re}{\left(x_{1}\right)} + i \operatorname{im}{\left(x_{1}\right)}$$
x23 = -I*re(x1) + im(x1)
$$x_{23} = - i \operatorname{re}{\left(x_{1}\right)} + \operatorname{im}{\left(x_{1}\right)}$$
x24 = -im(x1) + I*re(x1)
$$x_{24} = i \operatorname{re}{\left(x_{1}\right)} - \operatorname{im}{\left(x_{1}\right)}$$
x24 = i*re(x1) - im(x1)