We use cookies to improve your experience on our site and to show you relevant advertising. By browsing this website, you agree to our use of cookies. Learn more   

AtoZmath.com
Support us
(New) All problem can be solved using search box
I want to sell my website www.AtoZmath.com with complete code
Home What's new College Algebra Games Feedback About us
Algebra Matrix & Vector Numerical Methods Statistical Methods Operation Research Word Problems Calculus Geometry Pre-Algebra


Home > Algebra calculators > If x+1/x=2 then find x-1/x, x^2+1/x^2, x^2-1/x^2, x^3+1/x^3, x^3-1/x^3, x^4+1/x^4, x^4-1/x^4 example
1. If `x+1/x=2`, then find `x-1/x` example ( Enter your problem )
( Enter your problem )
  1. If `x+1/x = 2`, then others
  2. If `x-1/x = 6`, then others
  3. If `x^2+1/x^2 = 2`, then others
 		Other related methods
  1. If `x+1/x = 2`, then find `x-1/x`
  2. If `x+y = 5` and `x-y = 1`, then find `x^2+y^2`
  3. If `x+y+z = 1` and `x^2+y^2+z^2 = 29`, then find `xy+yz+zx`
  4. If `x+y+z=1,xy+yz+zx=-1` and `xyz=-1` then find `x^3+y^3+z^3`
2. If `x-1/x = 6`, then others
(Next example)

1. If `x+1/x = 2`, then others


1. If `x+1/x = 2`, then find `x^2+1/x^2`

Solution:
Here `x+1/x=2`


Now, We know that
`x^2+1/x^2=(x+1/x)^2-2`

`:.x^2+1/x^2=2^2-2`

`:.x^2+1/x^2=4-2`

`:.x^2+1/x^2=2`

2. If `x+1/x = 2`, then find `x^3+1/x^3`

Solution:
Here `x+1/x=2`


Now, We know that
`x^3+1/x^3=(x+1/x)^3-3(x+1/x)`

`:.x^3+1/x^3=2^3-3*2`

`:.x^3+1/x^3=8-6`

`:.x^3+1/x^3=2`

3. If `x+1/x = 2`, then find `x^4+1/x^4`

Solution:
Here `x+1/x=2`


Now, We know that
`x^2+1/x^2=(x+1/x)^2-2`

`:.x^2+1/x^2=2^2-2`

`:.x^2+1/x^2=4-2`

`:.x^2+1/x^2=2`


Now, We know that
`(x^4+1/x^4)=(x^2+1/x^2)^2-2`

`:.(x^4+1/x^4)=2^2-2`

`:.(x^4+1/x^4)=4-2`

`:.x^4+1/x^4=2`

4. If `x+1/x = 2`, then find `x-1/x`

Solution:
Here `x+1/x=2`


Now, We know that
`(x-1/x)^2=(x+1/x)^2-4`

`:.(x-1/x)^2=2^2-4`

`:.(x-1/x)^2=4-4`

`:.(x-1/x)^2=0`

`:.x-1/x=0`

5. If `x+1/x = 2`, then find `x^2-1/x^2`

Solution:
Here `x+1/x=2`


Now, We know that
`(x-1/x)^2=(x+1/x)^2-4`

`:.(x-1/x)^2=2^2-4`

`:.(x-1/x)^2=4-4`

`:.(x-1/x)^2=0`

`:.x-1/x=0`


Now, We know that
`(x^2-1/x^2)=(x-1/x) (x+1/x)`

`:.(x^2-1/x^2)=0*2`

`:.x^2-1/x^2=0`

6. If `x+1/x = 2`, then find `x^3-1/x^3`

Solution:
Here `x+1/x=2`


Now, We know that
`(x-1/x)^2=(x+1/x)^2-4`

`:.(x-1/x)^2=2^2-4`

`:.(x-1/x)^2=4-4`

`:.(x-1/x)^2=0`

`:.x-1/x=0`


Now, We know that
`x^3-1/x^3=(x-1/x)^3+3(x-1/x)`

`:.x^3-1/x^3=0^3+3*0`

`:.x^3-1/x^3=0+0`

`:.x^3-1/x^3=0`

7. If `x+1/x = 2`, then find `x^4-1/x^4`

Solution:
Here `x+1/x=2`


Now, We know that
`(x-1/x)^2=(x+1/x)^2-4`

`:.(x-1/x)^2=2^2-4`

`:.(x-1/x)^2=4-4`

`:.(x-1/x)^2=0`

`:.x-1/x=0`


Now, We know that
`(x^2-1/x^2)=(x-1/x) (x+1/x)`

`:.(x^2-1/x^2)=0*2`

`:.x^2-1/x^2=0`


Now, We know that
`x^2+1/x^2=(x+1/x)^2-2`

`:.x^2+1/x^2=2^2-2`

`:.x^2+1/x^2=4-2`

`:.x^2+1/x^2=2`


Now, We know that
`(x^4-1/x^4)=(x^2-1/x^2) (x^2+1/x^2)`

`:.(x^4-1/x^4)=0*2`

`:.x^4-1/x^4=0`



This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then Submit Here


2. If `x-1/x = 6`, then others
(Next example)


Share this solution or page with your friends.


Home What's new College Algebra Games Feedback About us
 
Copyright © 2024. All rights reserved. Terms, Privacy
 
 

.