SOLUTION: if x=1/{2+sqrt( 3 )} ,then (3x-x^3)/(1-3x^3) =?

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Question 975739: if x=1/{2+sqrt( 3 )} ,then (3x-x^3)/(1-3x^3) =?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
if x=1/{2+sqrt( 3 )} ,then (3x-x^3)/(1-3x^3) =?
x%22%22=%22%221%2F%282%2Bsqrt%28+3+%29%29%22%22%2A%22%22%282-sqrt%283%29%29%2F%282-sqrt%283%29%29%22%22=%22%22%282-sqrt%283%29%29%2F%284-3%29%22%22=%22%22%282-sqrt%283%29%29%2F1%22%22=%22%222-sqrt%283%29
 
x%5E3%22%22=%22%22%282-sqrt%283%29%29%5E3%22%22=%22%22%282-sqrt%283%29%29%282-sqrt%283%29%29%282-sqrt%283%29%29%22%22=%22%22%282-sqrt%283%29%29%284-4sqrt%283%29%2B3%29%22%22=%22%22
%282-sqrt%283%29%29%287-4sqrt%283%29%29%22%22=%22%2214-15sqrt%283%29%2B12%22%22=%22%2226-15sqrt%283%29

Substitute for x and x3 in
 
%283x-x%5E3%29%2F%281-3x%5E3%29%22%22=%22%22%283%282-sqrt%283%29%29-%2826-15sqrt%283%29%29%29%2F%281-3%2826-15sqrt%283%29%29%29%22%22=%22%22
%286-3sqrt%283%29-26%2B15sqrt%283%29%29%2F%281-78%2B45sqrt%283%29%29%22%22=%22%22%28-20%2B12sqrt%283%29%29%2F%28-77%2B45sqrt%283%29%29%22%22=%22%22%28-20%2B12sqrt%283%29%29%2F%28-77%2B45sqrt%283%29%29%22%22%2A%22%22%28-77-45sqrt%283%29%29%2F%28-77-45sqrt%283%29%29%22%22=%22%22
%281540-24sqrt%283%29-1620%29%2F%285929-6075%29%22%22=%22%22%28-80-24sqrt%283%29%29%2F%28-146%29%22%22=%22%22%28-8%2810%2B3sqrt%283%29%29%29%2F%28-146%29

Divide top and bottom by -2

%284%2810%2B3sqrt%283%29%29%29%2F73 or you can write that as

expr%284%2F73%29%2A%2810%2B3sqrt%283%29%29 if you prefer.

Edwin