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
Lilit [14]
3 years ago
7

If X²⁰¹³ + 1/X²⁰¹³ = 2, then find the value of X²⁰²² + 1/X²⁰²² = ?​

Mathematics
1 answer:
enyata [817]3 years ago
6 0

Step-by-step explanation:

\bf➤ \underline{Given-} \\

\sf{x^{2013} + \frac{1}{x^{2013}} = 2}\\

\bf➤ \underline{To\: find-} \\

\sf {the\: value \: of \: x^{2022} + \frac{1}{x^{2022}}= ?}\\

\bf ➤\underline{Solution-} \\

<u>Let us assume that:</u>

\rm: \longmapsto u =  {x}^{2013}

<u>Therefore, the equation becomes:</u>

\rm: \longmapsto u +  \dfrac{1}{u}  = 2

\rm: \longmapsto \dfrac{  {u}^{2} + 1}{u}  = 2

\rm: \longmapsto{u}^{2} + 1 = 2u

\rm: \longmapsto{u}^{2} - 2u + 1 =0

\rm: \longmapsto  {(u - 1)}^{2} =0

\rm: \longmapsto u = 1

<u>Now substitute the value of u. We get:</u>

\rm: \longmapsto {x}^{2013}  = 1

\rm: \longmapsto x = 1

<u>Therefore:</u>

\rm: \longmapsto {x}^{2022}  +  \dfrac{1}{ {x}^{2022} }  = 1 + 1

\rm: \longmapsto {x}^{2022}  +  \dfrac{1}{ {x}^{2022} }  = 2

★ <u>Which is our required answer.</u>

\textsf{\large{\underline{More To Know}:}}

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² - b² = (a + b)(a - b)

(a + b)³ = a³ + 3ab(a + b) + b³

(a - b)³ = a³ - 3ab(a - b) - b³

a³ + b³ = (a + b)(a² - ab + b²)

a³ - b³ = (a - b)(a² + ab + b²)

(x + a)(x + b) = x² + (a + b)x + ab

(x + a)(x - b) = x² + (a - b)x - ab

(x - a)(x + b) = x² - (a - b)x - ab

(x - a)(x - b) = x² - (a + b)x + ab

You might be interested in
What is g(x)?.......
8090 [49]

Answer:

g(x) = -|x|

Step-by-step explanation:

Are you familiar with the absolute value function y = |x|?

Its graph is v-shaped and opens up.

If the graph is turned upside down (so that it opens down), then g(x) = -|x|.

7 0
3 years ago
Can someone answer this correctly pls
AleksandrR [38]

Answer:

i = 45% and ii = 47% (Rounded)

Step-by-step explanation:

Simply divide 27 by 60 to get i:

27/60=.45

Convert to a percent chance.

.45=45%

Then divide 395 by 840 to get ii:

395/840=.47

Convert to a percent chance.

.47=47%

8 0
2 years ago
Anyone know this plzzzz hellpppp!?!!!!
Elena-2011 [213]
Y=4^4-100=16-100=-84
Result is -84
4 0
3 years ago
you are purchasing a house 12 years from now the estimated purchase price is $171,600 you want to make a 20% down payment how mu
IRINA_888 [86]

Answer:The answer would be $238.33 a month

7 0
3 years ago
A group of students at a high school took a standardized test. The number of students who passed or failed the exam is broken do
Anuta_ua [19.1K]

Answer:

Since P(male)xP(fail) = 0.0549 and and P(male and fail) = 0.0773, the two results are different, so the events are not independent.

Step-by-step explanation:

Independent events:

Two events, A and B are independent, if:

P(A \cap B) = P(A)P(B)

Probability of male:

58 + 14 = 72 males out of 58 + 14 + 98 + 11 = 181

So

P(male) = 72/181 = 0.3978

Probability of failling:

14 + 11 = 25 students fail out of 181. So

P(fail) = 28/181 = 0.1381

Multiplitication of male and failling:

0.3978*0.1381 = 0.0549

Probability of being male and failing:

14 out of 181. So

14/181 = 0.0773

Different probabilities, so not independent.

Since P(male)xP(fail) = 0.0549 and and P(male and fail) = 0.0773, the two results are different, so the events are not independent.

5 0
3 years ago
Other questions:
  • What decimal can be added to 0.0545454... To get 0.1545454
    11·2 answers
  • Is 2x + 8 = 2(x + 4) a infinite solution
    10·2 answers
  • Eddy drilled into a piece of wood and a joist to attach them. If he drilled 3 inches and the wood was 1 1/3 inches thick, how fa
    10·2 answers
  • Hi can someone help me with this?
    13·1 answer
  • Find the inverse of function f. f(x) = 1/2x +7 / <img src="https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7B2%7Dx%20%2B%207"
    8·1 answer
  • Please help find missing angle
    13·2 answers
  • Alex has 7 pounds of birdseed and 5 bird feeders.
    10·1 answer
  • Is it possible for a triangle to have the three angle measurements 7cm, 24cm, 25cm and is it congruent or not?
    15·1 answer
  • On a multiple choice test, problem 1 has four answer choices and problem 2 has three choices. Each problem has only one correct
    5·1 answer
  • PLSSS HELLLPPP MEE!!
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!