Show that if x, y, z are integers such that x^3+5y^3 = 25z^3, then x = y = 0.

Answers

Answer 1

Answer:

3125*k^9 + y^3 is an integer my closure property.

 but 5^(1/3) is not an integer, which forces z to be irrational.

Note that there is no way an integer value can rationalize 5^(1/3)

Step-by-step explanation:

x^3 = 25z^3 - 5y^3

x^3 = 5 ( 5z^3 - y^3)

x  =  (5 ( 5z^3 - y^3) )^(1/3) must be an integer

  = 5^(1/3) * (5z^3 - y^3)^(1/3)

Then  (5z^3 - y^3)^(1/3) = 25*k^3 for some integer k

 5z^3 - y^3 = 15625*k^9

 5z^3 = 15625*k^9 + y^3

  z^3 = 3125*k^9 + (1/5)*y^3

z =  ( 3125*k^9 + (1/5)*y^3 )^ ( 1/3)


Related Questions

HURRY!! WILL MARK BRAINLIEST!!!
whixhxh two points on the number line are opposites? !!HURRY WILL CASHAPP 10 BUCKS. ​

Answers

Points A and D are opposites.

Answer:

points a and d because point a is -1 and 2/3 and point d is 1 and 2/3 so they are opposites

The spinner shown below is used to play a game.
4
5
3
6
2
7
1
8
What is the probability that the arrow will land on a number greater than 5?
3/5
3/8
5/8
1/3​

Answers

The probability is 3/8

PLEASE HELP! I’ll GIVE THE BRAINLIEST TO WHOEVER ANSWERS CORRECTLY!!

Answers

Answer:

The answers 15

Step-by-step explanation:

You just subtract Q1 from Q3

So for the first its: 45 - 30 = 15

and the second one is 50 - 35 = 15

Answer choices for both of them are
A) linear
B) exponential
C) quadratic

Answers

Answer:

#16 is linear but idk what 17 is

70% of Mr. Austin's students like Geometry. 35% like both Algebra and Geometry. What percent of those who like Geometry also like Algebra?

A. 50%


B. 35%


C. 70%


D. 30%

Please help I’ll give branliest answer

Answers

Answer:

Either Impossible question or B

Step-by-step explanation:

2 Ideas...

B because the question states that 35% like both Algebra and Geometry. The question then goes on to ask "What percent of those who like Geometry also like Algebra?" which is stated in the above (35%)

Or...

It is a trick question (although that isn't an option so it is less likely)

Because 75+35 = more than 100

Hope this helps

I will give brainliest to the first person who answers.

Answers

Answer:

the answer is [tex]\sqrt{5\\}[/tex] , and - [tex]\sqrt{5\\}[/tex] which is C.

Step-by-step explanation:

well I got that answer by doing this

we have [tex]x^{2}[/tex]= 5

For [tex]x^{2}[/tex]= f (a) the solutions are x = [tex]\sqrt{f(a)\\}[/tex] , - [tex]\sqrt{f(a)\\}[/tex]

so in this case the solutions are [tex]\sqrt{5\\}[/tex], and - [tex]\sqrt{5\\}[/tex]

HOPE THIS HELPS :)

DUE NOW PLZ HELP
6, 9, 3, 7, 8, 7, 5
minimum:
maximum:

Answers

Answer:

minimum is 3 and maximum is 9

Step-by-step explanation:

your min is 3 and ur max is 9

convert the mixed number to an improper fraction. enter your answer below using the slash mark ( / ) as the fraction bar.
4/frac{1}{8}

Answers

33/8 is the correct answer

What are some good note for Notes for Median and mean

Answers

Answer:

To find the Median arrange the data in order from least to greatest then find the middle number. To find the middle number cross of one from the front and one from the bcak. If there are 2 numbers left in the middle add those numbers together and them divided the sum by 2.

The mean is the average of the numbers. It is easy to find. First,  add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.

Step-by-step explanation:

Which expression should replace the box to finish the expanded form of 387.926?


2 × 1100

20

0.02

20 × 110

Answers

Answer:

0.02

(or 2 x 1/100)

Step-by-step explanation:

Number:

387.926

The number '2' in this number is in the hundredth place.

*Remember, it is a decimal so in expanded form it is multiplied by a fraction*

Therefore, it is written as 2 x 1/100 or 0.02

Answer:

its 2x1/100

Step-by-step explanation:

i got it correct

Function A is represented by the equation

y=1/3x+5. Function B is represented by the graph. Which function has a greater rate of change? explain.

Answers

Answer:

They have the same rate of change.

Step-by-step explanation:

Well the graph of Function B is y = 1 / 3x + 2

So they have the same rate of change, since they have the same slope.

There are 450 total students at Snowden School. On Tuesdays, 12% of the students stay after school for Comedy Club. How many students stay after school for Comedy Club?​

Answers

Answer:

54 students

Step-by-step explanation:

First, change the percent to a decimal.

12% = 0.12

Now, multiply the decimal by the total amount of students to find the amount of students that stay after school.

450 × 0.12 = 54

54 students stay after school for Comedy Club.

Answer:

3750

Step-by-step explanation:

You have to do is divided 450 from 12% and then you get your answer

Does anyone know the answer? thank you!​

Answers

Answer:

x= c - b / 3a

Step-by-step explanation:

3ax + b = c

3ax = c - b

x= c - b / 3a

I need help please as soon as possible

Answers

Answer:

0

Step-by-step explanation:

1 1/8 + 1/8 is 1 2/8 or 1 1/4

you subtract 1 1/4 minus 5/4 which is 1 1/4

Answer:

0

Step-by-step explanation:

9/8 + 1/8 = 10/8

5/4-5/4 = 0

Sara has x dollars and Dina has 15 dollars less than Sara . Together the number

of dollars they have is?

Answers

Answer:

2x-15

Step-by-step explanation:

Sara has x dollars

dina has 15 less which is

x-15

together it will be

x+x-15

=2x-15

PLZ HELP I NEED THE RIGHT ANSWER ASAP!!!!!!!!

Answers

Answer:

B. 66

Step-by-step explanation:

[tex]\frac{1}{x}(2x + 192)[/tex]       Substitute x = 3

[tex]\frac{1}{3} (2 *3+192)[/tex]    Multiply in the parentheses

[tex]\frac{1}{3}[/tex](6 + 192)          Add

[tex]\frac{1}{3}[/tex](198)                Multiply

66

10 over 13 as a decimal rounded to the nearest tenth

Answers

Answer:

0.7

Step-by-step explanation:

If you divide 10 by 13 you get 0.76923 which rounded to the nearest tenth is 0.7

Hope this helped!

Answer:

0.8

Step-by-step explanation:

To find the decimal form of [tex]\frac{10}{13}[/tex] you'll need to divide 10 by 13.

10 ÷ 13 = 0.76923076923

The tenths decimal place is one to the right of the decimal: 0.1

Because the number after the tenths place is greater than or equal to 5, we will round the 0.7 up to a 0.8

The diameter of a circle measures 8 cm. What is the circumference of the circle?
Use 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.

Answers

Answer:

16π or 50.266

Step-by-step explanation:

Circumference formula is just 2πr ,and the radius is 8, so just sub into the formula

Answer: 25.12 cm

Step-by-step explanation:

The formula for the circumference of a circle is [tex]2\pi r[/tex], when r = the radius.

Diameter = 2 x radius = 8 cm. Therefore, the radius = 4 cm.

Plug r = 4 cm in to the circumference formula: [tex]2\pi (4)[/tex] = 8 x 3.14 = 25.12 cm.

The table shows values of f(x) What is f(2)? f(x) = 4, 2, 3, 9, 1 x= 0, 1, 2, 3, 4

Answers

I’m confused ???can you post the table that they provide you with?

there's no way to answer this because you didn't specify the domain and range (x,y)

Which logarithmic equation is equivalent to the exponential equation below?
ea = 35
A. log35 2 = e
B. In 35 = a
c. log235 = 2.5
D.. In a = 35

Answers

Answer:

B

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

[tex]e^{a}[/tex] = 35, then

[tex]log_{e}[/tex] 35 = a, that is

ln35 = a → B

I think id c that what i think(:($(::;(;:::);;);).-)(/-:

Sandra found the difference of 12.7 – 4.705. She added the difference to 1.06. What is her final answer?

Answers

Answer:

9.055

Step-by-step explanation:

12.7 - 4.705 = 7.995

7.995 + 1.06 = 9.055

Answer:

9.055

Step-by-step explanation:

12.7 - 4.705 = 7.995

7.995 + 1.06 = 9.055

what is the measure of angle 15

Answers

Answer:

A

Step-by-step explanation:

m<15 = m<1 because of how the transversals are placed. so m<1 = 90º - 65º = 25º

that means that m<15=25º

Answer:

<15=25º

Step-by-step explanation:

big brain

Help looks like i forgot to read a ruler

Answers

Answer: 4 1/16

Step-by-step explanation:

4/1//16 i think that

Tami would like to withdraw $10,364.10 at the end of each year, for 10 years, from an account paying 2.3% compounded annually. Determine the amount needed in the account for Tami to do this. Round to the nearest cent. a. $115,052.98 b. $103,641.00 c. $91,651.92 d. $93,759.91 Please select the best answer from the choices provided A B C D

Answers

Answer:

Answer:

Option c -$91,651.92

Step-by-step explanation:

Given : Tami would like to withdraw $10,364.10 at the end of each year, for 10 years, from an account paying 2.3% compounded annually.

To find : Determine the amount needed in the account for Tami to do this.    

Solution :

We apply the present value formula to get the amount,

     

Where, PV is the present value ,the required amount

P is the principal P=$10,364.10

r is the rate r=2.3% annually, r=0.023

n is the time n=10 years

Substitute in the formula,

   

   

   

   

     

     

Therefore, The amount needed is $91651.92.

Hence, Option c is correct.

Read more on Brainly.com - https://brainly.com/question/3432251#readmore

Step-by-step explanation:

100 points i will mark brainliest for fist correct answer

Answers

Answer:

Equal, equal, not equal, not equal

Step-by-step explanation:

A) Equal, because they have the same height and base. To find the area of a triangle, you use "(b+h)/2". In this situation, the "b" and the "h" are equal.

B) Equal, as they also have the same height and base. To find the area, you use b*h, and they are equivalent.

C) Not equal. The two lengths given are not equal.

D) Not equal. The two triangle's heights are equal, but their bases are not. If you look at the second triangle, you can see that if is further from the triangles' intersections. This means that the base is larger than the one on the left.

Maya can run 18 miles in 3 hours, and she can bike 18 miles in 2 hours.

What is Maya’s biking speed?

PLZ HELP IN A BIG RUSH PLZ PLZ PLZ

Answers

Answer:

Maya's biking speed is 8 miles per hour.

Step-by-step explanation:

She can run 18 miles in 3 hours. That means she could run 6 miles in one hour. So, if she can ride her bike 18 miles in 2 hours she can bike 9 miles per hour.

If she bikes for 27 (3 hours) miles and runs 9 miles (1.5 hours) then taking the total of miles dividing it by the time you would get Maya's speed.

Below are the average incomes for different education levels. How does the outlier affect the mean?mm

Answers

Answer:

It affects the Mean by how many different numbers.

Step-by-step explanation:

Find the medianDetermine all of your answers. and Figure out if the mean and the outlier are similiar.

Given: m arc AB = 4x, m arc BC = 3x
m arc CD = 2x, m arc DA = 3x
Find: m∠APB

Answers

Answer:

a > m/bp

Step-by-step explanation:

flip the equation

abp > m

divide both sides with bp

abp/bp > m/bp

a > m/bp

Answer:

m<APB = 30 degrees

Step-by-step explanation:

The sum of angles in a circle is 360 degrees. Add up all the arcs to get the equation : 4x+3x+2x+3x=360 degrees.

x is equal to 30 degrees

m arc AB = 4x = 120 degrees

m arc DC = 2x = 60 degrees

By secants exterior angles, m<APB = 1/2(m arc AB - m arc DC) = 1/2(120-60) = 30 degrees.

The answer is m<APB = 30 degrees

HELPPP

If x=-1, which quadrant does the point (2x,-x) lie in?

Answers

Answer:

Second

Step-by-step explanation:

x=-1

(2x, -x)

(2*-1, - -1)

(-2 ,1)

(negative, positive) is in the second quadrant

II      |       I

-------|----------------

III      |      IV

Please help due in 20 minutes!

Answers

Answer:

x =12

Step-by-step explanation:

We use the Pythagorean theorem

a^2 + b^2 =c^2 where a and b are the legs and c is the hypotenuse

x^2 + 5^2 = 13^2

x^2 +25 =169

Subtract 25 from each side

x^2 +25-25=169-25

x^2 = 144

Take the square root of each side

sqrt(x^2) = sqrt(144)

x = 12

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