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
Keith earns $37.00 in 4 hours. How much would he earn in 11 hours?
Leona [35]

Answer:

C

Step-by-step explanation:

37/4= 9.25

9.25*11 =101.75

7 0
2 years ago
Read 2 more answers
What is the 10th of a quarter of 1600
mihalych1998 [28]

Answer:

40

Step-by-step explanation:

A quarter of 1600 is 400. A tenth of that is 40.

:P

4 0
2 years ago
Read 2 more answers
Question 9
True [87]

Answer:

17

Step-by-step explanation:

m<1 = (4x + 2)

m<3 = (5x - 15)

To find the value of x, we need to generate an equation.

<1 and <3 are vertical angles. Vertical angles are congruent. Therefore:

m<1 = m<3

(4x + 2) = (5x - 15)

Use this equation to solve for x

4x + 2 = 5x - 15

Subtract 5x from both sides

4x + 2 - 5x = 5x - 15 - 5x

-x + 2 = -15

Subtract 2 from both sides

-x + 2 - 2 = -15 - 2

-x = -17

Divide both sides by -1

x = 17

5 0
2 years ago
If the base number is 2/3 and the power is 5.
solniwko [45]

Answer:

32/243

Step-by-step explanation:

do 2 to the 5th and put it above 3 to the 5th

3 0
2 years ago
Read 2 more answers
Please solve and show step by step
MissTica
The answer to the question

8 0
3 years ago
Other questions:
  • Two people are looking up at the Eiffel Tower. The people are 8 miles apart, and the Eiffel Tower is between them. The angle of
    5·1 answer
  • Convert (CAB) 16 to decimal<br><br>need help asap
    8·2 answers
  • Please help me with this
    12·1 answer
  • The formula for the area of a triangle is A = kbh, where A is the area, b is the base
    13·1 answer
  • What do you notice about the graph when it passess through a root of even multiplicity?​
    14·1 answer
  • Fill in the blank to make an equivalent answer ___:30=3.5​
    9·2 answers
  • Free brainiest to the first person to say anything.
    9·1 answer
  • What is the solution to 4(x+2)&gt;8x-3
    6·2 answers
  • Mary wants to join a gym.
    13·1 answer
  • PLEASE HELP HAVE TO GET DONE BEFORE 12!!
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!