If x+1/x= 3, then prove that m^5+1/m^5= 123

Answers

Answer 1

9514 1404 393

Explanation:

We can start with the relations ...

  [tex]\displaystyle\left(x+\frac{1}{x}\right)^3=\left(x^3+\frac{1}{x^3}\right)+3\left(x+\frac{1}{x}\right)\\\\\left(x+\frac{1}{x}\right)^5=\left(x^5+\frac{1}{x^5}\right)+5\left(x^3+\frac{1}{x^3}\right)+10\left(x+\frac{1}{x}\right)\\\\\textsf{From these, we can derive ...}\\\\x^5+\frac{1}{x^5}=\left(x+\frac{1}{x}\right)^5-5\left(\left(x+\frac{1}{x}\right)^3-3\left(x+\frac{1}{x}\right)\right)-10\left(x+\frac{1}{x}\right)[/tex]

  [tex]\displaystyle x^5+\frac{1}{x^5}=\left(x+\frac{1}{x}\right)^5-5\left(x+\frac{1}{x}\right)^3+5\left(x+\frac{1}{x}\right)\right)\\\\x^5+\frac{1}{x^5}=3^5 -5(3^3)+5(3)\\\\=((3^2-5)3^2+5)\cdot3=(4\cdot9+5)\cdot3=(41)(3)\\\\=\boxed{123}[/tex]


Related Questions

Find the slope of the line through the points (2, 16) & (18, 1)

Answers

Answer:

-15/16

Step-by-step explanation:

PLS HELPPPPPPPPPP PLSSSSSS ASAP

Answers

Answer:

3 i think

uhh I don't know, I forgot about this

Apply the distributive property to simplify -1/3 (12+30) . A. 14 B. 6 C. -13 D. -14

Answers

Answer: -14

(− 1/ 3 )(12+30)

=  −1 /3 (12+30)

=  −1/ 3 (42)

= −14

Answer:

I answered this on accident sorry

Step-by-step explanation:

help help help pls pls​

Answers

Answer:

x ≈ 7.1

Step-by-step explanation:

The circumference of this circle is 2πx.

65/360 of that circumference is said to be 8

so we can solve x from

65/360 · 2πx = 8

which can be simlified to

2πx = 8 · 360/65

πx = 288/13

x = 288 / (13π) ≈ 7.1

Tim has some marbles.
Sue has twice as many marbles as Tim.
Jim has 15 marbles.
Tim, Sue and Jim have the a total of 63 marbles.
How many marbles does Tim have?​

Answers

Let x = the number of marbles Tim has
Let 2x = the number of marbles Sue has
x + 2x + 15 = 63
3x = 48
x = 16 marbles


Tayler works at a bicycle shop. When he sells a bicycle, he earns 6% of the sale price as a commission One day Tayler sold 1 bicycle for $125 and 2 bicycles for $75 cach What was the total amount o
commission he earned?
HELP......

Answers

The answer is $16.50

Jet bought a computer that was 20% off. If the original price of the computer was $785, how much did Jet save? How much did Jet pay?

Answers

785·20%=157

785-157=628

Answer:

You will pay $628 for a item with original price of $785 when discounted 20%. In this example, if you buy an item at $785 with 20% discount, you will pay 785 - 157 = 628 dollars.

4x+5-x=10+3x+4
solution

Answers

Answer:

9

Step-by-step explanation:

4x-x=3x

3x±5=10±3x±4

10±4=14

14±3x

3x±5=14±3x

3x-3x=14-5

3x-3x=0

14-5=9

PLEASE HELP URGENT WILL MARK AS BRAINLIEST PLUS POINTS!!

Answers

Answer:

22 (4th option)

Step-by-step explanation:

The side lengths are useless.

Pay attention to the angles.

<QRP=68 degrees.

Vertical angles make it so <SRT=68

180-90(right angle)-68=22 degrees

HELP DUE IN 2 MINUTES

Answers

Answer:

6

Step-by-step explanation:

add them all together which will get you 24

then divide by the number of months

24/4=6


If you are offered an investment that pays 3.5% simple interest, and you plan to invest for 4 years, about how much do you have
invest to end up earning at least $500?
AY
$1755
B)
$2496
$3572
D)
$4328

Answers

Answer:

$3572

Step-by-step explanation:

Answer:

C.) 3572

Step-by-step explanation:

I Just took the test

I will give you brainliest! Please help me

Answers

Answer:

A) 7x^5 + 2x^2 + 6

Step-by-step explanation:

I hope this helps.

Answer:

The answer is A

Pls help me. Sorry, it's so easy.

Answers

Answer:

he bought 36 hot dogs

4 packs of hot dogs

3 packs of buns

Step-by-step explanation:

Answer:

He bought 36 hot dogs,4 packs of them, and 3 packs of buns

Step-by-step explanation:

The LCM (least common multiple) of 9 and 12 is 36 and 12*3=36 and 9*4=36 so they are even

There are
questions on the Aspire English test.
A. 20
B. 65
C. 35
D. 50cc

Answers

Answer:

Answer is 50cc Number D

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

3.4.2

Please Help ASAP
Which value of x is a solution to this equation?
2x^2 - 4x + 16 = 0
A. X = 3
B. X = -2
C. X = -3
D. X = 2

Answers

9514 1404 393

Answer:

  no solution

Step-by-step explanation:

The discriminant is ...

  b^2 -4ac = (-4)^2 -4(2)(16) = 16 -128 = -112

A negative discriminant means there are no real solutions to the equation.

_____

The complex solutions are 1±i√7.

If we assume the equation has a typographical error and is intended to be ...

  2x^2 -4x -16 = 0

The solutions are x = -2 and x = 4.

slove for x for the triangle

Answers

Answer:

3x+2+36=110

3x= 110-38= 72

x= 72/3=24

Step-by-step explanation:

The value of a stock increases by 8% each year.
1. Explain why the stock value does not increase by 80% each decade.
2. Does the value increase by more or less than 80% each decade?

Answers

Answer:

if it increases 8% each year, the next year it's not 8% of the original, but 8% of the 108% and so forth.

The increase after 10 years is (108%)^10 - 100% which is bigger than 80%.

If the value of a stock increases by 8% each year, then, that is not equal to the value of a stock increases 80% each decade.

What is Percentage Increase?

The degree to which a value increases expressed in percent form is known as percentage increase.

Given that, The value of a stock increases by 8% each year.

a) If it increases 8% each year, the next year it's not 8% of the original, but 8% of the 108% and so forth, the incasement in percentage is an exponential increase not a linear increase, so we can't say that, the value of the stock increases 80% each decade

b) Since,  (108%)¹⁰ > 80%

Hence, the increase after 10 years is (108%)¹⁰, will be bigger than 80%.

Hence, If the value of a stock increases by 8% each year then, that is not equal to the value of a stock increases 80% each decade

For more references on percentage increase, click;

https://brainly.com/question/27992848

#SPJ2

A countertop is 11 feet long and 4 fee t wide.

What is the area of the countertop in square meters? Use the conversion 1 foot = 0.305 meter. Round your
final answer to 2 decimal place

Answers

Answer:

4.09m^2

Step-by-step explanation:

A countertop is 11 feet long and 4 fee t wide.

Using the conversion

1foot = 0.305 meter

11fet = 11(0.305)

11feet = 3.355 m

4 feet= 4 * 0.305

4feet = 1.22m

Area of the countertop = Length * Width

Area of the countertop = 3.355 * 1.22

Area of the countertop = 4.0931m^2

Hence the required area is 4.09m^2 to 2 decimal places

Determine the quadrant in which the terminal side of theta lies.

Answers

Answer:

A) 2nd quadrant

B) 2th quadrant

Step-by-step explanation:

hope this helps have a nice day!!

38 divided by 8. Show ALL work for credit. NO WORK NO CREDIT
:((

Answers

Answer:

38 / 8 is 4.75

Step-by-step explanation:

Um I tried putting a photo of my work but it wouldn't let me sorry ;-;

the diameter of a circle is 8 ft. Find the circumferenceto the nearest tenth.

Answers

Answer:

25.1 ft

Step-by-step explanation:

To solve for circumference is pretty simple. Just use the equation 2pi r (r=radius, radius is diameter divided by 2).

So essentially, apply to your calculator:

2(3.14)4=25.12

pretty simple! hope this helps!

Marcia is using base ten blocks to multiply decimals. He is using the flat to represent one whole.
one whole
Which of the following multiplication expressions is Marcia representing below?

Answers

Answer:

nice

Step-by-step explanation:

which answer choice is equivalent to the expression (x+2)^2 - 6x+2?
a. x^2 - 2x+8x
b. x^2 - 2x+6
c. x^2 - 6x+4
d. -5x^2 +6

Answers

Answer:

(x+2)^2 - 6x+2

(x+2)^2 = (x+2).(x+2)

            = x(x+2) + 2(x+2)

           = xx + x2 + 2x +4 ( x2 = 2x)

           = x^2+ 4x +4

(x+2)^2 - 6x+2

x^2+ 4x +4- 6x+2

x^2+ 4x - 6x+2 +4

x^2- 2x+2 + 6 (b)

Step-by-step explanation:

Among the following, which one is not in similarity theorem.
A. SSS similarity theorem
B. SS similarity theorem
C. SAS similarity theorem
D. AA similarity theorem​

Answers

Answer:

If two triangles are similar it means that all corresponding angle pairs are congruent and all corresponding sides are proportional. However, in order to be sure that two triangles are similar, you do not necessarily need to have information about all sides and all angles.

Jenny wants to buy a pair of pants that cost $35. The pants are on sale for
25% off.
What is the total cost of the discounted pants?

Answers

Answer:

35 / 4 = 8.75

35 - 8.75 = 26.25

I hope you a great life. Till we meet again, Farewell!

Write as a single number. log464 + log536

Answers

Answer:

1000

Step-by-step explanation:

- 1/5 + 3/5 I know it looks easy but show the work!

Answers

The answer is 2/5

-1/5 + 3/5
(-1) + 3
————
5
=2/5

how much sugar should farid use for 1/2 of a batch of muffins

Answers

Answer:

3/8

Step-by-step explanation:

.

Answer: the answers would be 3/8

Step-by-step explanation:

Got it right

Robin has a collection of dimes, nickels and quarters. He has 4 times as many dimes as nickels. He has 20 more quarters than nickels. The
ratio of the number of dimes to the number of quarters is 3:2. Which equation can be used to calculate the number of nickels, n, Robin
has?
OA
Exh
8:33
acer

Answers

Answer: Robin has 50 nickels, 60 dimes, and 120 quarters.

Step-by-step explanation:

Factor the expression using the GCF. Explain your reasoning using math
vocabulary.
24xy – 16y

Please help!

Answers

Answer:

8y(3x - 2)

Step-by-step explanation:

8y is the GCF so I divided it out and set it outside the parenthesis.

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