makaylathomas30 makaylathomas30
  • 03-03-2015
  • Mathematics
contestada

solve each equation by finding all roots
X^4-81=0

Respuesta :

konrad509
konrad509 konrad509
  • 03-03-2015
[tex]x^4-81=0 \\ (x^2)^2-9^2=0\\ (x^2-9)(x^2+9)=0\\ (x-3)(x+3)(x^2+9)=0\\ x=3 \vee x=-3[/tex]
Answer Link
apologiabiology
apologiabiology apologiabiology
  • 03-03-2015
so this is a difference of 2 perfect squares
so if
x^2-y^2 then it is equal to (x-y)(x+y)

so
x^4-81=[(x^2)^2]-[(9)^2]=(x^2-9)(x^2+9)

so we know if xy=0 then x or/and y=0 so assume that they are equal to zero

x^2+9=0
we can't do anything about this because
x^2=-9
and that is not possible in the real realm


x^2-9=0
yet another difference of 2 perfect squares
x^2-3^2=(x-3)(x+3)=0
set them to zero
x-3=0
x=3
x+3=0
x=-3

so x=3 or -3
Answer Link

Otras preguntas

All parts in Noh dramas were played by women
a=h(b+c) solve for c
What value of the variable makes the statement true? m + 4 = –2.8 a. –6.8 b. –1.2 c. 1.2 d. 6.8
How would someone divide $8.40➗ 6? How do you divide this I'm confused like what do I use the long way or short way? Option one: 6)~~~~~~ 8.40 Option tw
If Teresa's daughter is my daughter's mother, what am I to Teresa?
A bus travels 20 km in 30 minutes. what is the average speed of the bus?
What is 31 less than fifty two million and four
Express the number 20000 as a single digit integer times a power of 10
I need to write the number 36 in expanded form
Why are scientific models important? a. they prove scientific theories. b. they help visualize thing that are very complex. very large. and very small c. they m