|
|
|
|
|
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 )
|
|
|
3. If `x^2+1/x^2 = 2`, then others
1. If `x^2+1/x^2 = 2`, then find `x-1/x`
Solution:
Here `x^2+1/x^2=2`
Now, We know that
`(x-1/x)^2=(x^2+1/x^2)-2`
`:.(x-1/x)^2=2-2`
`:.(x-1/x)^2=0`
`:.x-1/x=0`
2. If `x^3+1/x^3 = 2`, then find `x+1/x`
Solution:
Here `x^3+1/x^3=2`
Now, We know that
`(x+1/x)^3=(x^3+1/x^3)+3(x+1/x)`
`:.(x+1/x)^3-3(x+1/x)=(x^3+1/x^3)`
`:.(x+1/x)^3-3(x+1/x)=2`
`:.y^3-3y -2=0`, where `y=(x+1/x)`
clearly, y=2 satisfies `y^3-3y -2=0`
`:.x+1/x=2`
3. If `x^3-1/x^3 = 2`, then find `x-1/x`
Solution:
Here `x^3-1/x^3=2`
Now, We know that
`(x-1/x)^3=(x^3-1/x^3)-3(x-1/x)`
`:.(x-1/x)^3+3(x-1/x)=(x^3-1/x^3)`
`:.(x-1/x)^3+3(x-1/x)=2`
`:.y^3+3y -2=0`, where `y=(x-1/x)`
clearly, y=2 satisfies `y^3+3y -2=0`
`:.x-1/x=2`
4. If `x^4+1/x^4 = 2`, then find `x-1/x`
Solution:
Here `x^4+1/x^4=2`
Now, We know that
`(x^2+1/x^2)^2=(x^4+1/x^4)+2`
`:.(x^2+1/x^2)^2=2+2`
`:.(x^2+1/x^2)^2=4`
`:.x^2+1/x^2=2`
Now, We know that
`(x-1/x)^2=(x^2+1/x^2)-2`
`:.(x-1/x)^2=2-2`
`:.(x-1/x)^2=0`
`:.x-1/x=0`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
|
|
|
|
Share this solution or page with your friends.
|
|
|
|
