Step-by-step explanation:
![\bf➤ \underline{Given-} \\](https://tex.z-dn.net/?f=%20%5Cbf%E2%9E%A4%20%5Cunderline%7BGiven-%7D%20%5C%5C%20)
![\sf{x^{2013} + \frac{1}{x^{2013}} = 2}\\](https://tex.z-dn.net/?f=%5Csf%7Bx%5E%7B2013%7D%20%2B%20%5Cfrac%7B1%7D%7Bx%5E%7B2013%7D%7D%20%3D%202%7D%5C%5C)
![\bf➤ \underline{To\: find-} \\](https://tex.z-dn.net/?f=%20%5Cbf%E2%9E%A4%20%5Cunderline%7BTo%5C%3A%20find-%7D%20%5C%5C%20)
![\sf {the\: value \: of \: x^{2022} + \frac{1}{x^{2022}}= ?}\\](https://tex.z-dn.net/?f=%5Csf%20%7Bthe%5C%3A%20value%20%5C%3A%20of%20%5C%3A%20x%5E%7B2022%7D%20%2B%20%5Cfrac%7B1%7D%7Bx%5E%7B2022%7D%7D%3D%20%3F%7D%5C%5C)
![\bf ➤\underline{Solution-} \\](https://tex.z-dn.net/?f=%20%5Cbf%20%E2%9E%A4%5Cunderline%7BSolution-%7D%20%5C%5C%20)
<u>Let us assume that:</u>
![\rm: \longmapsto u = {x}^{2013}](https://tex.z-dn.net/?f=%20%5Crm%3A%20%5Clongmapsto%20u%20%3D%20%20%7Bx%7D%5E%7B2013%7D%20)
<u>Therefore, the equation becomes:</u>
![\rm: \longmapsto u + \dfrac{1}{u} = 2](https://tex.z-dn.net/?f=%20%5Crm%3A%20%5Clongmapsto%20u%20%2B%20%20%5Cdfrac%7B1%7D%7Bu%7D%20%20%3D%202)
![\rm: \longmapsto \dfrac{ {u}^{2} + 1}{u} = 2](https://tex.z-dn.net/?f=%20%5Crm%3A%20%5Clongmapsto%20%5Cdfrac%7B%20%20%7Bu%7D%5E%7B2%7D%20%2B%201%7D%7Bu%7D%20%20%3D%202)
![\rm: \longmapsto{u}^{2} + 1 = 2u](https://tex.z-dn.net/?f=%20%5Crm%3A%20%5Clongmapsto%7Bu%7D%5E%7B2%7D%20%2B%201%20%3D%202u)
![\rm: \longmapsto{u}^{2} - 2u + 1 =0](https://tex.z-dn.net/?f=%20%5Crm%3A%20%5Clongmapsto%7Bu%7D%5E%7B2%7D%20-%202u%20%2B%201%20%3D0)
![\rm: \longmapsto {(u - 1)}^{2} =0](https://tex.z-dn.net/?f=%20%5Crm%3A%20%5Clongmapsto%20%20%7B%28u%20-%201%29%7D%5E%7B2%7D%20%3D0)
![\rm: \longmapsto u = 1](https://tex.z-dn.net/?f=%20%5Crm%3A%20%5Clongmapsto%20u%20%3D%201)
<u>Now substitute the value of u. We get:</u>
![\rm: \longmapsto {x}^{2013} = 1](https://tex.z-dn.net/?f=%20%5Crm%3A%20%5Clongmapsto%20%7Bx%7D%5E%7B2013%7D%20%20%3D%201)
![\rm: \longmapsto x = 1](https://tex.z-dn.net/?f=%20%5Crm%3A%20%5Clongmapsto%20x%20%3D%201)
<u>Therefore:</u>
![\rm: \longmapsto {x}^{2022} + \dfrac{1}{ {x}^{2022} } = 1 + 1](https://tex.z-dn.net/?f=%20%5Crm%3A%20%5Clongmapsto%20%7Bx%7D%5E%7B2022%7D%20%20%2B%20%20%5Cdfrac%7B1%7D%7B%20%7Bx%7D%5E%7B2022%7D%20%7D%20%20%3D%201%20%2B%201)
![\rm: \longmapsto {x}^{2022} + \dfrac{1}{ {x}^{2022} } = 2](https://tex.z-dn.net/?f=%20%5Crm%3A%20%5Clongmapsto%20%7Bx%7D%5E%7B2022%7D%20%20%2B%20%20%5Cdfrac%7B1%7D%7B%20%7Bx%7D%5E%7B2022%7D%20%7D%20%20%3D%202)
★ <u>Which is our required answer.</u>
![\textsf{\large{\underline{More To Know}:}}](https://tex.z-dn.net/?f=%5Ctextsf%7B%5Clarge%7B%5Cunderline%7BMore%20To%20Know%7D%3A%7D%7D)
(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
Answer:
aₙ = 0.2(-0.3)⁽ⁿ⁻¹⁾
Step-by-step explanation:
The geometric sequence with the first term a, a common ratio r has the nth term given as
Tₙ = arⁿ⁻¹
where Tₙ is the nth term
From the given sequence
a = 0.2
r = -0.06/0.2
= -0.3
Hence the nth term
= 0.2 * -0.3ⁿ⁻¹
The right option is E
Answer:
1 hour
Step-by-step explanation:
No. of pages print in 1.5 hours = 900
dividing LHS and RHS by 1.5 so that we get 1 hour in LHS
no. of page print in 1.5/1.5 (1) hours = 900/1.5 = 600.
Thus, it takes 1 hour to print 600 pages.
Given that we have to find how
long will it take her to print a book of 600 pages.
Answer is 1 hour.