- #1
musicgold
- 304
- 19
- Homework Statement
- This is not a homework problem. I am stuck
- Relevant Equations
- The attached picture shows the figure and the equation I am trying to solve.
I seem to have stuck with this simple algebra problem.$$ \frac {(L - 2.r)^2 } { L^2} = 1/2 $$
$$ 2( L^2 + 4r^2 - 4rL) = L^2 $$
$$ L^2 + 8 r^2 - 8r L = 0 $$
$$ (L - 2 \sqrt 2 r )^2 = 8rL - 4\sqrt 2. rL $$
$$ (L - 2 \sqrt 2 r )^2 = 4rL. (2 -\sqrt 2) $$
I don't know how to proceed from here to get
$$ L = ( 4 + 2\sqrt 2 ) . r $$
$$ 2( L^2 + 4r^2 - 4rL) = L^2 $$
$$ L^2 + 8 r^2 - 8r L = 0 $$
$$ (L - 2 \sqrt 2 r )^2 = 8rL - 4\sqrt 2. rL $$
$$ (L - 2 \sqrt 2 r )^2 = 4rL. (2 -\sqrt 2) $$
I don't know how to proceed from here to get
$$ L = ( 4 + 2\sqrt 2 ) . r $$
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