1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Wittaler [7]
3 years ago
15

Find the solutions to x⁴-64=0 and the x-intercepts of the graph of y=x⁴-64.

Mathematics
1 answer:
Setler [38]3 years ago
3 0

Answer:

1. x_1=2\sqrt{2}\\x_2=-2\sqrt{2}\\x_3=i2\sqrt{2}\\x_4=-i2\sqrt{2}

2. A=(2\sqrt{2},0) and B=(-2\sqrt{2},0)

Step-by-step explanation:

We have the expression x^4-64=0 to find the solutions we have to clear x. Then,

x^4-64=0 Add 64 in both sides of the equation.

x^4-64+64=64\\x^4=64

Now we have to re-write the equation:

u=x^2⇒u^2=(x^2)^2\\u^2=x^4

Then,

u^2=64

Apply square root on both members

\sqrt{u^2}=\sqrt{64}\\u=8 , u=-8

Now substitute back u=x^2

1. x^2=8

2. x^2=-8

Solving for x:

1. x=+\sqrt{8}=\sqrt{2^3}=\sqrt{2^2}.\sqrt{2}\\x=2\sqrt{2}\\or\\x=-\sqrt{8}\\x=-2\sqrt{2}

2. x=+\sqrt{-8}=\sqrt{(-1).8} =\sqrt{-1}\sqrt{8} \\x=i\sqrt{8}\\x=i.2\sqrt{2} \\or\\x=-\sqrt{-8}\\x=-i.2\sqrt{2}

Then the solutions for x^4-64=0 are:

x_1=2\sqrt{2}\\x_2=-2\sqrt{2}\\x_3=i2\sqrt{2}\\x_4=-i2\sqrt{2}

To find the x intercepts of the graph y=x^4-64 we have to replace with y=0.

This means: x^4-64=0

We already found the solutions for the expression, but we have to consider only the real solutions.

x_1=2\sqrt{2}\\x_2=-2\sqrt{2}

Because in a graph we can't have imaginary solutions.

Then the x intercepts of the graph are:

A=(2\sqrt{2},0) and B=(-2\sqrt{2},0)

The graph of the function is:

You might be interested in
(Will give Brainliest, these are angle relationships) Please help, and show work, what relationship is it and set up an equation
aalyn [17]

Answer:

27

Step-by-step explanation:

5x+12=147

=147-12

135=5x

135/5

x=27

6 0
2 years ago
Read 2 more answers
The manager of the toy store at the mall is curious about why nobody is buying the new robot toys. He's very annoyed because he
marin [14]

Answer: B

Step-by-step explanation: I believe it's B because if you're able to get the opinions of others about your store. You'll be able to see whats the customers are more interested in, so therefore be able to supply your store with stuff people are more intrigued in. (Let me know if I'm wrong, have a good day)

6 0
3 years ago
!please help!<br> what is 22/22-12/22?
inn [45]
22/22-12/22= 10/22
Which can be simplified as 5/11
4 0
2 years ago
-y (2 - 5y + 4)<br> Simplify plz
Neko [114]

This equation simplified would be

-y(-5y+6)

3 0
3 years ago
Read 2 more answers
Mackenzie's company reimburses her $0.75 per mile that she drives for business. If she goes on a business trip and drives a tota
lesantik [10]

Answer:90

Step-by-step explanation:

:)

6 0
3 years ago
Other questions:
  • A parking garage charges $3 for each of the first three hours. After three hours, the charge is $7 an hour. What is the total co
    9·2 answers
  • How many times does 64 go into 1760?
    14·2 answers
  • How to solve 2 2/6 +4 3/6
    7·2 answers
  • 3x+2y=8
    13·1 answer
  • Latoya is on her way home in her car. She has driven 30 miles so far, which is five-sixths of the way home. What is the total le
    11·2 answers
  • One factor in flood safety along a levee is the area that will absorb water should the levee break. The coordinates that make up
    7·2 answers
  • Please answer and show steps please show steps please show steps 10 points
    13·1 answer
  • Am I colorblind? please help
    13·2 answers
  • What is this called, like whats the name of this thing??<br> {18 ≤ y ≤ 30}
    11·1 answer
  • Determine the unit rate of the following. 9 yards of material for 5 dresses The unit rate isyd / dress (Type a whole number or a
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!