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
Eduardwww [97]
2 years ago
13

2x² - 5x+1 has roots alpha and beta. Find alpha⁴+beta⁴ without solving the equation.

Mathematics
1 answer:
shepuryov [24]2 years ago
7 0

Answer:

Step-by-step explanation:

\alpha+\beta=\dfrac{5}{2} \\\\\alpha*\beta=\dfrac{1}{2} \\\\\alpha^2+\beta^2=\dfrac{21}{4} \ (see\ previous\ post)\\\\(\alpha+\beta)^4=\dfrac{625}{16} \\\\=\alpha^4+\beta^4+4*\alpha^3*\beta+6*\alpha^2*\beta^2+4*\alpha*\beta^3\\\\=\alpha^4+\beta^4+4*(\alpha*\beta)(\alpha^2+\beta^2)+6*\alpha^2*\beta^2\\\\\alpha^4+\beta^4=(\alpha+\beta)^4-4*(\alpha*\beta)(\alpha^2+\beta^2)-6*\alpha^2*\beta^2\\\\= \dfrac{625}{16} -4*\dfrac{1}{2} *\dfrac{21}{4} -6*(\dfrac{1}{2})^2 \\\\

= \dfrac{625}{16}- \dfrac{168}{16}-\dfrac{24}{16}\\\\\\= \dfrac{433}{16}

You might be interested in
Before a sale, an item’s price was $38.00; during the sale, it was 15% off. What was the sale price?
Pani-rosa [81]
38 times (1-15%)
$32.3
4 0
3 years ago
Help me pls i dont understand math
e-lub [12.9K]

Answer:

c = -6

Step-by-step explanation:

Let us solve your equation step-by-step, which is this: c /−3  + 5 = 7

The first step is to simplify both sides of the equation: −1 /3 c + 5 = 7

Then, subtract 5 from both sides: -1/3c + 5 - 5 = 7 - 5 ---> -1/3c = 2

Multiply both sides by -3/1 making it equal to: c = -6.

4 0
3 years ago
Which number line shows the solution to the inequality 8x – 9 < –41?
lora16 [44]

Answer:

A

Step-by-step explanation:

In the inequality, you want to simplify it to get x on one side, and the numeric values on the other.

So, moving 9 to the other side, you get, 8x<-32

Then, you can divide by 8 on both sides to get x alone.

You get, x<-4.

From this, we can see that it should be an open dot at -4, and pointing to the left.

So, the correct number line is A.

7 0
2 years ago
3.305 + 1.7 what's the sum? Also more questions are coming just doing a test
Paraphin [41]

  3.305

 +1.7

  5.005

Line up the decimal points and add like you usually would add.

5.005 is the answer.

5 0
3 years ago
Dawn comma Sergio comma Tyrone comma and Jim have all been invited to a dinner party. They arrive randomly and each person arriv
professor190 [17]

Answer:

a. 24

b. 2

c. 0.0833 = 8.33%

Step-by-step explanation:

a.

The first "slot" of person to arrive has 4 possibilities, then the second "slot" will have 3 possibilities, as one has already arrived, then the third "slot" has 2 possibilities, and the fourth "slot" has just 1 possibility.

So, multiplying all these combinations, we have 4*3*2*1 = 24 possible ways they can arrive

b.

If the first and the last person are already "locked", we just have possibilities for the second and third person. The second will have 2 possibilities (Sergio or Tyrone), and the third will have only 1 (the person that wasn't the second between Sergio and Tyrone). So, the number of possibilities is 2*1 = 2

c.

If we have 2 cases where Dawn is first and Jim is last, from a total of 24 possible cases, the probability is 2/24 = 1/12 = 0.0833 = 8.33%

3 0
3 years ago
Other questions:
  • Please explain to me how to answer this question
    8·1 answer
  • Jack knows the surface area of a cylinder and its radius. He wants to find the cylinder's height. He needs to rewrite the formul
    9·2 answers
  • What is the solution of this equation?<br> -1y = -4
    7·1 answer
  • 15 POINTS!
    9·2 answers
  • 4 quarts = how many cups
    11·2 answers
  • One number exceeds another number by 6. One fourth of the sum of the two numbers is two less than the smaller.
    5·1 answer
  • Which set of Ordered pairs represent y as a function of x
    6·1 answer
  • I need help with my Algebra 1 ugh plz help! Sorry there’s a typo
    13·1 answer
  • His grandmother is sick, so Hassan is making a pot of bean soup to bring for dinner. The recipe calls for equal amounts of 3 kin
    15·1 answer
  • It takes Sue, Jeff and Todd 4 hours to paint a room together. If it takes Sue 10 hours by herself and Jeff 12 hours by himself,
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!