Better Students Ask More Questions.
If x^3 + 1/x^3 = 10, then find x + 1/x.
1 Answer | add yours
You need to write an alternate form of the given expression `x^3 + 1/x^3 = 10` such that:
`x^3 + 1/x^3 = 10 => x^6 + 1 = 10x^3`
Using the following substitution yields:
`x^3 = t => x^6 = t^2`
Changing the variable yields:
`t^2 - 10t + 1 = 0`
You should use quadratic formula such that:
`t_(1,2) = (10+-sqrt(100-4))/2`
`t_(1,2) = (10+-4sqrt(6)/2 => t_(1,2) = 5+-2sqrt6`
You should substitute `x^3` for `t` such that:
`x^3 = 5+-2sqrt6 => x = root(3)(5+-2sqrt6)`
You may evaluate `x + 1/x` such that:
`x + 1/x =root(3)(5+-2sqrt6) + 1/(root(3)(5+-2sqrt6))`
Hence, evaluating the expression `x + 1/x` yields `x + 1/x = root(3)(5+-2sqrt6) + 1/(root(3)(5+-2sqrt6)).`
Posted by sciencesolve on October 19, 2012 at 2:52 PM (Answer #1)
Join to answer this question
Join a community of thousands of dedicated teachers and students.