cosatica18
cosatica18 cosatica18
  • 26-03-2021
  • Mathematics
contestada

What is the solution when the equation wx^2 + w=0 is solved for x, where w is a positive integer?​

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kuellar
kuellar kuellar
  • 26-03-2021

Answer:

[tex]x=i[/tex]

(i.e., [tex]x[/tex] is a complex number)

Step-by-step explanation:

We have

[tex]wx^2+w=w(x^2+1)=0[/tex]

Then it must be that

[tex]x^2+1=0[/tex]

as we are told [tex]w[/tex] is a positive integer (i.e., [tex]w\neq 0[/tex]), then it follows that

[tex]x^2=-1[/tex]

which is the definition of the unit imaginary number ([tex]i^2=-1[/tex]), so we may conclude:

[tex]x=i[/tex]

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