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
stepladder [879]
3 years ago
7

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

Mathematics
1 answer:
alina1380 [7]3 years ago
7 0

9514 1404 393

Explanation:

We can start with the relations ...

  \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)

  \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}

You might be interested in
Log 3(x+5)- log 3(x-3) = 2
inessss [21]

Answer:

x = 4

Step-by-step explanation:

solate the variable by dividing each side by factors that don't contain the variable.

7 0
3 years ago
Read 2 more answers
GR5_Math_U7_FS
Nutka1998 [239]

Answer:

4/6 of a pizza.

Step-by-step explanation:

We know that:

Both pizzas are of the same size.

Jasmine cut her's into 12 slices.

Kelly cut her's into 6 slices, and ate 2 slices, then Kelly ate 2/6 of a pizza.

Jasmine ate X of a pizza, and we know that between them ate a total of 1 pizza.

This means that:

X of a pizza + 2/6 of a pizza = 1 pizza

X + 2/6 = 1

X = 1 - 2/6

X = 6/6 - 2/6 = 4/6

Jasmine ate 4/6 of a pizza, knowing that she cut her's into 12 slices, this would mean that she ate 8/12 of a pizza, or 8 slices.

5 0
2 years ago
Find the length of the altitude to the hypotenuse of a right triangle whose sides have lengths 10, 24, 25.
chubhunter [2.5K]
I DONT KNOW BUT I SURE AS HELL KNOW IM HIGH ON HYPOTENUSE...<span />
8 0
3 years ago
In the number 9440 how many times greater is the 4 marked x more Han 4 marked y
allsm [11]
I dont even know what your asking 
4 0
3 years ago
2 x ( __ x 7 ) - ( __ x 6 )
Maslowich
That acc makes no sense
7 0
3 years ago
Read 2 more answers
Other questions:
  • The number of students in each of the seventh grade homerooms that volunteer in the office are shown in the table. use mental ma
    14·1 answer
  • 50 POINTS!!!!!!
    12·1 answer
  • Exponential function
    6·1 answer
  • Which term best describes two events in which knowledge of one event has no effect on the probability of the other event?
    15·1 answer
  • The following show a change of scale made by an architect in one of his drawings. Old: 1 inch = 16 meters. New: 1 inch = 2 meter
    12·2 answers
  • 2-3/4z=1/8z+9 please show your steps!
    7·1 answer
  • Help please, giving brainlist to anyone who answers
    15·1 answer
  • Find the volume of the complex figure below.
    5·2 answers
  • A bag contains 2 white balls, 3 red balls and a black ball. if a ball is selected at random, what is the probability that it is
    9·2 answers
  • A line intersects the point (-11, 4) and has a slope of -2. What are the inputs to the point-slope formula? y - [?] = [](x-[])​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!