Question

How would I solve for x?\[\frac{3}{x^2}=\frac{1}{(x-d)^2}\]where d is a constant.

Answer 1

start with
\[3(x-d)^2=x^2\] and solve the quadratic

Answer 2

that's what I can't remember how to do!

Answer 3

\[3(x^2-2dx+d^2)=x^2\]
\[3x^2-6dx+3d^2=x^2\]
\[2x^2-6dx+3d^2=0\] etc

Answer 4

right, I don't know what I was thinking haha. no reason the d should have confused me. just to make sure, all I would do is this right? \[x=\frac{6d\pm \sqrt{36d^2-24d^2}}{4}\]\[x=\frac{1}{2}\left(3d\pm\sqrt{3}d\right)\]

Answer 5

thats correct :)