SOLUTION: Find the real solutions by factoring. x^2 + sqrt{3}x^2 - 3 = 0 Let x^4 = (x^2)^2 Let u = x^2 u^2 + sqrt{3}x - 3 = 0 Stuck here.... Can I use the q

Algebra ->  Radicals -> SOLUTION: Find the real solutions by factoring. x^2 + sqrt{3}x^2 - 3 = 0 Let x^4 = (x^2)^2 Let u = x^2 u^2 + sqrt{3}x - 3 = 0 Stuck here.... Can I use the q      Log On


   

Question 1207666: Find the real solutions by factoring.


x^2 + sqrt{3}x^2 - 3 = 0


Let x^4 = (x^2)^2

Let u = x^2

u^2 + sqrt{3}x - 3 = 0

Stuck here....

Can I use the quadratic formula?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Your starting equation is THIS

    x%5E2 + sqrt%283%29%2Ax%5E2 - 3 = 0.


It is the same as

    x%5E2 + sqrt%283%29%2Ax%5E2 = 3.


Factor left side

    x%5E2%2A%281%2Bsqrt%283%29%29 = 3.


Divide both sides by  %281%2Bsqrt%283%29%29  and express x^2 explicitly

    x^2 = 3%2F%281%2Bsqrt%283%29%29.


Get rid of irrationality in the denominator

    x^2 = 3%2F%28sqrt%283%29%2B1%29 = %283%2F%28sqrt%283%29%2B1%29%29%2A%28%28sqrt%283%29-1%29%2F%28sqrt%283%29-1%29%29 = %283%2A%28sqrt%283%29-1%29%29%2F%283-1%29 = %283%2F2%29%2A%28sqrt%283%29-1%29.


Now take square root of both sides and find x

    x = sqrt%28%283%2F2%29%2A%28sqrt%283%29-1%29%29 = 1.047891...


ANSWER.  x = sqrt%28%283%2F2%29%2A%28sqrt%283%29-1%29%29 = 1.047891  (rounded).

Solved.