project-euler / project-euler / 137 / analysis.txt

Diff from to

project-euler/137/analysis.txt

 x/(2*$s) * { (1+$s)/[1 - x(1+$s)/2] - (1-$s)/[1 - x(1-$s)/2] } =
 
 x/(2*$s) * { 1/[1/(1+$s) - x/2] - 1/[1/(1-$s) - x/2] } =
+
+    [y = x/2]
+
+y*$s * {1/[1/(1+$s) - y] - 1/[1/(1-$s) - y] } =
+
+    [z = 1/y]
+
+$s * { 1 / [z/(1+$s) - 1] - 1 / [z/(1-$s) - 1] } = N
+
+$s * [z/(1-$s)-1 - z/(1+$s) + 1 ]/[z/(1+s)-1]/[z/(1-s)-1] = N
+
+$s * z * (1/(1-$s)-1/(1+$s)) = N[z/(1+$s)-1][z/(1-s)-1]
+
+    [ * (1+$s) * (1-$s)]
+
+$s * $z * (1+$s-1+$s) = N[z-(1+$s)][z-(1-$s)]
+
+    2 $s^2 * $z = N [ z^2 - 2z + (1-$s^2)]
+
+    $s^2 = 5
+
+    10z = N [ z^2 - 2z - 4 ]
+
+    z^2 - (2+10/N)z -4 = 0
+
+    z = [ -2a +/- sqrt(b^2-4ac) ] / (2*a)
+
+
+
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