addisonrausch addisonrausch
  • 17-09-2019
  • Mathematics
contestada

Factor the expression over the complex numbers x^2+20

Factor the expression over the complex numbers x220 class=

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luchoprat
luchoprat luchoprat
  • 17-09-2019

Answer:

[tex](x - 2i\sqrt{5} )(x+2i\sqrt{5} )[/tex]

Step-by-step explanation:

To do that you need to use this:

[tex]x^{2} -y^{2} =(x-y)(x+y)[/tex]

In order to do the substraction you need to put a minus to 20

[tex]x^{2}+20 \\=x^{2} - (-20) \\=(x-\sqrt{-20} )(x+\sqrt{-20} ) \\=(x - 2i\sqrt{5} )(x+2i\sqrt{5} ); \\\\\\\sqrt{-20} =\sqrt{(-1)(2^{2})(5)} =2i\sqrt{5}[/tex]

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