Question 825746
the sum of a number and its reciprocal is thrice the difference of the number and its reciprocal.the number is
:
n + {{{1/n}}} = 3(n - {{{1/n}}})
n + {{{1/n}}} = 3n - {{{3/n}}}
mult both sides by n
n^2 + 1 = 3n^2 - 3
1 + 3 = 3n^2 - n^2
4 = 2n^2
divide both sides by 2
2 = n^2
n = {{{sqrt(2)}}}
I expected an integer, but it checked out on a calc both sides = 2.12132