Question

(-4/x^2)(sqrt(x^2+64))+(4/x+1) (x(x^2+64)^-1/2))=0
How do you solve for x? I'm having trouble with the algebra!!!

Answer 1

here is a visual of the equation: http://www.wolframalpha.com/input/?i=%28-4%2Fx%5E2%29%28sqrt%28x%5E2%2B64%29%29%2B%284%2Fx%2B1%29%28x%28x%5E2%2B64%29%5E-1%2F2%29%3D0

Answer 2

i know the answer is x=cube root 256. I just don't know how to get there.

Answer 3

what do you have so far

Answer 4

technically this is the furthest i have worked out a minimization problem so now i have to find x to plug it back to the original equation. I don't know how to go further than this

Answer 5

okay ... multbly x(4/x+1) and you will get (4+x)

Answer 6

then your eq.
(4+x)/(sqr(x^2+64) - 4sqr(x^2+64)/x^2=0

Answer 7

\[\left( 4+x \right)/\sqrt{x^2+64} - 4\sqrt{X^2 + 64}/ x^2\]

Answer 8

\[(x^2*(4+x)-4\sqrt{X^2+64}*\sqrt{x^2+64})/(x^2*\sqrt{x^2+64)}\]

Answer 9

\[4x^2+x^3-4x^2-4*64=0\]

Answer 10

x^3=4*64=256