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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
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1. If `x+1/x=2`, then find `x-1/x` example
( Enter your problem )
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2. If `x-1/x = 6`, then others
1. If `x-1/x = 6`, then find `x^2+1/x^2`
Solution:
Here `x-1/x=6`
Now, We know that
`x^2+1/x^2=(x-1/x)^2+2`
`:.x^2+1/x^2=6^2+2`
`:.x^2+1/x^2=36+2`
`:.x^2+1/x^2=38`
2. If `x-1/x = 6`, then find `x^3-1/x^3`
Solution:
Here `x-1/x=6`
Now, We know that
`x^3-1/x^3=(x-1/x)^3+3(x-1/x)`
`:.x^3-1/x^3=6^3+3*6`
`:.x^3-1/x^3=216+18`
`:.x^3-1/x^3=234`
3. If `x-1/x = 6`, then find `x^4+1/x^4`
Solution:
Here `x-1/x=6`
Now, We know that
`x^2+1/x^2=(x-1/x)^2+2`
`:.x^2+1/x^2=6^2+2`
`:.x^2+1/x^2=36+2`
`:.x^2+1/x^2=38`
Now, We know that
`x^4+1/x^4=(x^2+1/x^2)^2-2`
`:.x^4+1/x^4=38^2-2`
`:.x^4+1/x^4=1444-2`
`:.x^4+1/x^4=1442`
4. If `x-1/x = 6`, then find `x+1/x`
Solution:
Here `x-1/x=6`
Now, We know that
`(x+1/x)^2=(x-1/x)^2+4`
`:.(x+1/x)^2=6^2+4`
`:.(x+1/x)^2=36+4`
`:.(x+1/x)^2=40`
`:.x+1/x=6.32`
5. If `x-1/x = 6`, then find `x^2-1/x^2`
Solution:
Here `x-1/x=6`
Now, We know that
`(x+1/x)^2=(x-1/x)^2+4`
`:.(x+1/x)^2=6^2+4`
`:.(x+1/x)^2=36+4`
`:.(x+1/x)^2=40`
`:.x+1/x=6.32`
Now, We know that
`(x^2-1/x^2)=(x+1/x) (x-1/x)`
`:.(x^2-1/x^2)=6.32*6`
`:.x^2-1/x^2=37.95`
This material is intended as a summary. Use your textbook for detail explanation.
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