Hey Guys!
Try to solve this maths question.....
[tex]a + b + c = 4 \\ {a}^{2} + {b}^{2} + {c}^{2} = 10 \\ {a}^{3} + {b}^{3} + {c}^{3} = 22 \\ {a}^{4} + {b}^{4} + {c}^{4} = ? [/tex]
Don't copy from web and Don't spam
Need answer as well as explanation
Thank You!

Answers

Answer 1

Use the multinomial theorem to compute some polynomial expansions:

(a + b + c)² = a² + b² + c² + 2 (ab + ac + bc)

(a + b + c)³ = a³ + b³ + c³

… … … … … … + 3 (a²b + a²c + ab² + b²c + ac² + bc²)

… … … … … … + 6 abc

(a + b + c)⁴ = a⁴ + b⁴ + c⁴

… … … … … … + 4 (a³b + a³c + ab³ + b³c + ac³ + bc³)

… … … … … … + 6 (a²b² + a²c² + b²c²)

… … … … … … + 12 (a²bc + ab²c + abc²)

Now, given that

a + b + c = 4

a² + b² + c² = 10

it follows that

ab + ac + bc = (4² - 10)/2 = 3

We use this result to simplify the extra terms in the 3rd-degree expansion.

a²b + a²c + ab² + b²c + ac² + bc²

= a (ab + ac) + b (ab + bc) + c (ac + bc)

= a (ab + ac + bc) + b (ab + ac + bc) + c (ab + ac + bc) - 3abc

… … I underline the terms that are added and subtracted … …

= (a + b + c) (ab + ac + bc) - 3abc

= 4 • 3 - 3abc

= 12 - 3abc

Given that

a³ + b³ + c³ = 22

this tells us that

4³ = 22 + 3 (12 - 3abc) + 6abc

4³ = 58 - 3abc

and so

abc = (4³ - 58)/(-3) = -2

from which it follows that

a²b + a²c + ab² + b²c + ac² + bc² = 12 - 3 • (-2) = 18

Now we similarly simplify the extra terms in the 4th-degree expansion.

a³b + a³c + ab³ + b³c + ac³ + bc³

= a² (ab + ac) + b² (ab + bc) + c² (ac + bc)

= a² (ab + ac + bc) + b² (ab + ac + bc) + c² (ab + ac + bc) - a²bc - ab²c - abc²

= (a² + b² + c²) (ab + ac + bc) - (a²bc + ab²c + abc²)

= 10 • 3 - (a²bc + ab²c + abc²)

which means

4⁴ = a⁴ + b⁴ + c⁴

… … … … … … + 4 (30 - a²bc - ab²c - abc²)

… … … … … … + 6 (a²b² + a²c² + b²c²)

… … … … … … + 12 (a²bc + ab²c + abc²)

reduces to

136 = a⁴ + b⁴ + c⁴

… … … … … … + 6 (a²b² + a²c² + b²c²)

… … … … … … + 8 (a²bc + ab²c + abc²)

Now, we know a + b + c = 4 and abc = -2, so we have

a²bc + ab²c + abc² = abc (a + b + c) = -2 • 4 = -8

and so

136 = a⁴ + b⁴ + c⁴ + 6 (a²b² + a²c² + b²c²) + 8 • (-8)

200 = a⁴ + b⁴ + c⁴ + 6 (a²b² + a²c² + b²c²)

Finally, we know that ab + ac + bc = 3. Squaring this gives

(ab + ac + bc)² = 3²

a²b² + a²c² + b²c² + 2 (a²bc + ab²c + abc²) = 9

but we also know that a²bc + ab²c + abc² = -8, so

a²b² + a²c² + b²c² + 2 • (-8) = 9

a²b² + a²c² + b²c² = 25

Therefore, we end up with

200 = a⁴ + b⁴ + c⁴ + 6 • 25

⇒   [[[   a⁴ + b⁴ + c⁴ = 50   ]]


Related Questions

Which point is located in Quadrant III ?

(−1/2, 1/4)

(1/2, −1/4)

(−1/2, −1/4)

I will give you brainliest if you are right

Answers

Answer:

here you go :)

Quadrant lll is always both negative so the answer is (-1/2, -1/4)

Step-by-step explanation:

2x+x+x+2y times 3y times y

Answers

Answer:

4x+ 6y^2

Step-by-step explanation:

make q the subject of the formula

Answers

Answer:

q = 2p - 1/3

Step-by-step explanation:

2q + 2p = 1+5q

2q = 1+5q-2p

-3q=1-2p

-q = 1-2p/3

q= 2p-1/3

Answer:

q=[tex]\frac{2p-1}{3}[/tex]

Step-by-step explanation:

2(q+p)=1+5q

EXPAND BRACKET

2q+2p=1+5q

MINUS 2q FROM BOTH SIDES

2p=1+3q

MINUS 1 FROM BOTH SIDES

2p-1=3q

DIVIDE BOTH SIDES BY 3

[tex]\frac{2p-1}{3}[/tex]=q

Isolate f variable! Solve the equation algebraically! Show work!!

42 = 6f

Answers

Answer:

f=7

Step-by-step explanation:

42=6f

/6   /6

42/6=7

You divide 6 from 42, which leaves you with 7=f.

what is 2+2 i need help like rly bad i will give 100 points

Answers

Answer:

4 bestie <3

Step-by-step explanation:

Answer:

Step-by-step explanation:

4

Add 3 5/6+(−1 1/6). Write your answer as a mixed number in the simplest form.

Answers

The result of 3 5/6+(−1 1/6) is 2 2/3.

INTRODUCTION

The definition of a fraction is that the division of two integers by the number being divided is called the numerator and the divisor is called the denominator.

Kinds of Fractions:

a. Mixed fractions, for example: 1⅘, 2½, 3⅔, etc.b. Common fractions, for example: , , , etc.c. Percent fractions, for example: 50%, 2%, 6%, etc.d. Decimal fraction, for example: 0.50

DISCUSSION

3 5/6+(−1 1/6)

= 23/6 + (-7/6)

= 23/6 - 7/6

= 16/6

= 8/3

= 2 2/3

Conclusion:

So, The result of 3 5/6+(−1 1/6) is 2 2/3.

Learn more:

mampir ke indo :v

Example of Fraction Problem: https://brainly.co.id/task/14280048Example of Fraction Subtraction Problem: https://brainly.co.id/task/23345402Material about fractional equations: https://brainly.co.id/task/3304077

______

Answer Details:Grade: 4 Elementary SchoolSubject: MathMaterial: Chapter 6 -ShardsCategorization Code: 4.2.6

Keywords: Subtract mixed fractions.

[tex]2\frac{2}{3}[/tex] is the simplest form of expression  [tex]3\frac{5}{6} +(-1\frac{1}{6} )[/tex]

What is Fraction?

A fraction represents a part of a whole.

Fractions are three types proper fraction, improper fraction and Mixed fraction.

The given expression is [tex]3\frac{5}{6} +(-1\frac{1}{6} )[/tex]

Three five by six plus minus one one by six.

Let us convert mixed fraction to improper fraction and solve

[tex]3\frac{5}{6} +(-1\frac{1}{6} )[/tex]

(18+5)/6 -(6+1)/6

23/6-7/6

Now take LCM as 6

(23-7)/6

Sixteen by six

16/6

Eight by three

8/3

[tex]2\frac{2}{3}[/tex]

To learn more on Fractions click:

https://brainly.com/question/10354322

#SPJ2

Define algebra ? And give some examples..​

Answers

Answer:

Algebra is a abstract way of thinking about things. We usually see this by defining things we don't know as some sort of symbol (Matter of fact. All of Mathmatics revolves around symbols). It doesn't necessarily have to be a number. I could label some big brown sturdy thing with green stuff on top as a tree which in a mathmatical sense the tree would be the variable and the actual thing would be the thing inside of the variable. But basically it's an abstract way of thinking

Step-by-step explanation:

when a number is decreased by 3% the result is 80. what was the original number?

Answers

Answer:

82.47

Step-by-step explanation:

.93n = 80

n = 80/.93

n = 82.47

-10 + = -3 I need help

Answers

Answer:

the answer is

7

Step-by-step explanation:

why is it 7 it is cause -10+7=3

Answer:

7

the answer is 7 because -10+7=-3

I need help with this question,

Answers

The slope of the line would be 3/4

What is the value of q in the equation 49 - 2 = 39+8?
q
=
10
0 -
7
10
7
06
0 10

Answers

Answer:

The is no "q" in the equation provided.  If there is supposed to be, please add it.  Otherwise, q is undefined.  It can have any value.  I choose 0.

Step-by-step explanation:

3 tickets to the museum cost $12.75. At this rate, what is the cost of:
1 ticket?
5 tickets?

Answers

Answer:

1 ticket would be $4.25

5 tickets would be $21.25

Step-by-step explanation:

Hope that help, mind if a get a brainliest now?

Answer:

4.25 for 1 ticket, 21.25 for 5

Step-by-step explanation:

12.75 divided by 3 = 4.25 x 5 = 21.25

help me with this!!!

Answers

1
4
3
2
that’s the order

PLEASE HELP!! name the property of equality that the statement illustrates:

if x = y , then -2x = -2y

Answers

The multiplication property of equality states that if [tex]x=y[/tex] is true, then [tex]xz=yz[/tex] must also be true.

The property of equality illustrated by the statement "if x = y, then -2x = -2y" is the: Multiplication Property of Equality.

How to Identify the Property of Equality?

The properties of equality describe the relation between the two sides of an equation and state that the two sides remain equal even after applying the same arithmetic operation on each side.

The property of equality illustrated by the statement "if x = y, then -2x = -2y" is the Multiplication Property of Equality.

This property states that if you multiply both sides of an equation by the same nonzero number, the equality still holds true.

In this question, both sides of the equation are multiplied by -2, maintaining the equality between the expressions.

Read more about Property of Equality at: https://brainly.com/question/1601404

#SPJ3

How much does Janet earn per hour

Plz helppppp

Answers

Answer:

$7.50 per hour

Step-by-step explanation:

after 2 hours, she earns $15

after 4 hours, she earns $30

after 8 hours, she ears $60

15/2 = 30/4 = 60/8 = 7.5/1

[tex]\huge \dag \sf{Answer \: it}[/tex]​
[tex]solve \: for \: x \\ \\ {2}^{ {x}^{2} } 2 \frac{3x \sqrt{3} }{2} = 8 [/tex]
Don't spam and Don't copy.
Need answer with explanation
Don't answer if you don't know

Best of luck guys

Answers

Answer:

Answer: x = √3 and 8/(3√3)

Step-by-step explanation:

[tex]{ \rm{({2}^{ {x}^{2} } )(2 \frac{3x \sqrt{3} }{2}) = 8}}[/tex]

• For the first bracket:

[tex]{ \rm{ {2}^{ {x}^{2} } = 8}} \\ \\ { \rm{ {2}^{ {x}^{2} } = {2}^{3} }} \\ \\ { \rm{ {x}^{2} = 3}} \\ \\ { \rm{x = \pm \sqrt{3} }}[/tex]

• For the second bracket;

[tex]{ \rm{ 2 \frac{3x \sqrt{3} }{2} = 8}} \\ \\ { \rm{3x \sqrt{3} = 8 }} \\ \\ { \rm{3x = \frac{8}{ \sqrt{3} } }} \\ \\ { \rm{x = \frac{8}{3 \sqrt{3} } }}[/tex]

can somebody help me out which one is correct
A , B , C , D ?

Answers

Options A, B and D are true.

Hey y’all can u give me the correct answer pls.

Answers

Answer:

x > -7 (Hey man think before ask)

Step-by-step explanation:

It is so easy .....

Answer:

-6,-4,-2,3

Equation: x>−7

Step-by-step explanation:

Just ask.

Hope this helps.

11,046 as a decimal

Answers

Answer:

It cant be converted to decimal or fraction while it is a integer

A plant grows at a constant rate. The table shows the heights of the plant for different numbers of days of growth. Which of the following pairs of days and heights could also be included in the table? Select all that apply.

Answers

The answer is an answer that I do not know

Help please Pretty plz ​

Answers

Answer:1/10

Step-by-step explanation:

Start by multiplying 1/100 by 1/10

The answer will be 1/1000

What is the equation of the line that passes
through the points (3,-1) and (7, 3)?

Answers

Answer: y = 1x + -4

Equation of a straight line:

y = mx + b ------(i)

Step by Step Solution:

Step 1: Calculating Slope (m).

m = y2-y1 /x2-x1

m = 3--1 /7-3

m = 4/4

m = 1

Now putting value of m in equation (i)

y = 1x + b -----(ii)

Step 2: Calculating Y-intercept (b).

Lets choose the first point, (3,-1) for calculating y-intercept:

y = mx + b

-1 = 1(3) + b

-1 = 3 + b

-4 = b

b = -4

Now putting value of b in equation (ii)

y = 1x + -4

pls help i need help​

Answers

[tex](5^6)^0 \\\\=5^0\\\\=1[/tex]

Jesse collected 42 football cards and 28 baseball cards. Simplify the ratio of baseball cards to football cards in his collection

Answers

Answer:

3:2

Step-by-step explanation:

42:28

21:14

3:2

Given that the shape is a kite and Angle A=25, Angle C=85, what is Angle
D?

Answers

Answer:

m∠D = 165°

Step-by-step explanation:

∠B and ∠C are congruent, so ∠B = 85°

The angles of the kite all added together have to add up to 360°

85 + 85 + 25 + x = 360

195 + x = 360

x = 165

Answer:

m∠D = 165°

Step-by-step explanation:

∠B and ∠C are congruent, so ∠B = 85°

The angles of the kite all added together have to add up to 360°

85 + 85 + 25 + x = 360

195 + x = 360

x = 165

Find the slope for (4,5)and (2,3)

Answers

Answer:

1

Step-by-step explanation:

The slope of a line is (-1/2) and a point on the line is (-2, 3). Find the equation for the line in slope intercept form.

Answers

Answer:

y=-1/2x+2

Step-by-step explanation:

y-y1=m(x-x1)

y-3=-1/2(x-(-2))

y-3=-1/2(x+2)

y=-1/2x-2/2+3

y=-1/2x-1+3

y=-1/2x+2

A student says that it 5x^2 =20,then x must be
equal to 2. Do you agree or disagree with the
student? Justity your answer.

Answers

I agree with the student.Justification:[tex] {5x}^{2} = 20 \\ = > {x}^{2} = \frac{20}{5} \\ = > {x}^{2} = 4 \\ = > x = \sqrt{4} \\ = > x = 2[/tex]Therefore, x must be equal to 2.So his statement is right.

Hope you could get an idea from it.

Doubt clarification - use comment section.

What number multiplied by 3/5 has a product of 1?​

Answers

Answer:

5/3

Step-by-step explanation:

let the number be x

3/5×[x] = 3x/5

3x/5=1

x=1÷3/5

x=5/3

Pls help me
4(3-x)=6(x+2)+20

Answers

Answer:

x = -2

Step-by-step explanation:

Other Questions
4x + 60 + 5x = 100What is x? Please help me it's due in 5 minutes!! I will give brainliest! 9. Anna has 102 quarters. Jazmin has102 dimes. Who has more money, Annaor Jazmin? How much more? Explainyour reasoning. how long does it take cancer to efect the whole body The triangles pictured below are:Congruent by AASCongruent by AASCongruent by HLCongruent by HLCongruent by SSSCongruent by SSSCongruent by SASCongruent by SASCongruent by ASACongruent by ASANot CongruentNot Congruent IMAGE BELOW Choose which word fits the description. What would you not do at the store? mirar la ropa limpiar comprar cosas hablar con tu amigo. y using the two ways you have learned about between temperature, pressure and volume, what are two ways you could increase the gas pressure of a system. How does zora neale hurston use mrs. Turner to present a cultural criticism? she mocks mrs. Turners strict religious practices. She critiques mrs. Turners obsession with material wealth. She mocks mrs. Turners belief that everyone should look alike. She critiques mrs. Turners use of profane language. What were some of Maya Angelous purposes in writing I Know Why the Caged Bird Sings? Check all that apply.to tell about her childhoodto prompt readers to think about what growing up as an African American girl in poverty was liketo convince readers to move to Stamps, Arkansasto explain why it is important for people to own general storesto honor an important woman in her life What was the result of the Webster-Ashburton Treaty of 1842 Which best describes how to add 9.73 and 21.6? what do you do if your stumek hurts and you feel empty and dark and sad inside? kuz I feel that way At time t= 0, a storage tank is empty and begins filling with water. For t > 0 hours, the depth of the water in the tank is increasing at a rate of W (t) feet per hour. Which of the following is the best interpretation of the statement W' (2) > 3?a. Two hours after the tank begins filling with water, the depth of the water is increasing at a rate greater than 33 feet per hour.b. Over the first two hours after the tank begins filling with water, the depth of the water is always increasing at a rate greater than 3 feet per hour.c. Two hours after the tank begins filling with water, the rate at which the depth of the water is rising is increasing at a rate greater than 3 feet per hour per hour.d. Over the first two hours after the tank begins filling with water, the rate at which the depth of the water is rising is always increasing at a rate greater than 33 feet per hour per hour. help me here pls(solve on your own, a,b, and c)(more practice, a and b) Add and simplify 4/9 + 3/7 Question 2 options: 7/16 55/63 12/63 3/12 solve for x . Help me solve them ANSWER URGENTLY!!In 2016, France became the first country to ban grocery stores from discarding edible food. Should other countries do the same? What problems might this policy create? Which equation is modeled on the number line below? PLS HELP!!! WILL MARK BRAINLIEST!!