# project-euler

committed dc5b4ae

# 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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