El profesor se sorprenderá mucho al ver tu solución correcta😉
3 4 pi*n 2 / pi\ pi*n + ----- + x *|pi*n + --| - 2*x = 0 2 \ 2 /
a*x^2 + b*x + c = 0
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (pi/2 + pi*n) * (pi*n^4 + pi*n^3/2) = 4 - (2*pi + 4*pi*n)*(pi*n^4 + pi*n^3/2)
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
/ / _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ \ _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ \ / _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ \ _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | | / 2 2 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \ 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\\| / 2 2 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \ 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\\| | / 2 2 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \ 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\\| / 2 2 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \ 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\\ | | 4 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \\ / 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\ |atan2\- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)/, 4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)//|| 4 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \\ / 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\ |atan2\- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)/, 4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)//|| | 4 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \\ / 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\ |atan2\- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)/, 4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)//|| 4 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \\ / 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\ |atan2\- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)/, 4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)//| | 2*|2 - \/ \- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)// + \4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)// *cos|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||*im(n) \/ \- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)// + \4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)// *(1 + 2*re(n))*sin|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| (1 + 2*re(n))*|2 - \/ \- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)// + \4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)// *cos|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| 2*\/ \- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)// + \4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)// *im(n)*sin|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | \ \ 2 // \ 2 /| \ \ 2 // \ 2 / x1 = I*|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ \ pi*\(1 + 2*re(n)) + 4*im (n)/ pi*\(1 + 2*re(n)) + 4*im (n)/ / pi*\(1 + 2*re(n)) + 4*im (n)/ pi*\(1 + 2*re(n)) + 4*im (n)/
/ / _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ \ _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ \ / _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ \ _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | | / 2 2 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \ 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\\| / 2 2 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \ 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\\| | / 2 2 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \ 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\\| / 2 2 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \ 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\\ | | 4 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \\ / 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\ |atan2\- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)/, 4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)//|| 4 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \\ / 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\ |atan2\- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)/, 4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)//|| | 4 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \\ / 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\ |atan2\- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)/, 4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)//|| 4 / / 2 / 3 2 \ 2 / 3 3 \ 2 / 5 3 2 4 \\ / 2 / 3 2 \ 2 / 4 4 2 2 \ 2 / 5 2 3 4 \\ |atan2\- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)/, 4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)//| | 2*|2 + \/ \- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)// + \4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)// *cos|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||*im(n) \/ \- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)// + \4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)// *(1 + 2*re(n))*sin|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| (1 + 2*re(n))*|2 + \/ \- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)// + \4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)// *cos|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| 2*\/ \- pi *\- im (n) + 3*re (n)*im(n)/ - 4*pi *\- 4*im (n)*re(n) + 4*re (n)*im(n)/ - 4*pi *\im (n) - 10*im (n)*re (n) + 5*re (n)*im(n)// + \4 - pi *\re (n) - 3*im (n)*re(n)/ - 4*pi *\im (n) + re (n) - 6*im (n)*re (n)/ - 4*pi *\re (n) - 10*im (n)*re (n) + 5*im (n)*re(n)// *im(n)*sin|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | \ \ 2 // \ 2 /| \ \ 2 // \ 2 / x2 = I*|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ \ pi*\(1 + 2*re(n)) + 4*im (n)/ pi*\(1 + 2*re(n)) + 4*im (n)/ / pi*\(1 + 2*re(n)) + 4*im (n)/ pi*\(1 + 2*re(n)) + 4*im (n)/
x2 = (((-pi^2*(3*re(n)^2*im(n) - im(n)^3) - 4*pi^2*(4*re(n)^3*im(n) - 4*re(n)*im(n)^3) - 4*pi^2*(5*re(n)^4*im(n) - 10*re(n)^2*im(n)^3 + im(n)^5))^2 + (-pi^2*(re(n)^3 - 3*re(n)*im(n)^2) - 4*pi^2*(re(n)^4 - 6*re(n)^2*im(n)^2 + im(n)^4) - 4*pi^2*(re(n)^5 - 10*re(n)^3*im(n)^2 + 5*re(n)*im(n)^4) + 4)^2)^(1/4)*cos(atan2(-pi^2*(3*re(n)^2*im(n) - im(n)^3) - 4*pi^2*(4*re(n)^3*im(n) - 4*re(n)*im(n)^3) - 4*pi^2*(5*re(n)^4*im(n) - 10*re(n)^2*im(n)^3 + im(n)^5, -pi^2*(re(n)^3 - 3*re(n)*im(n)^2) - 4*pi^2*(re(n)^4 - 6*re(n)^2*im(n)^2 + im(n)^4) - 4*pi^2*(re(n)^5 - 10*re(n)^3*im(n)^2 + 5*re(n)*im(n)^4) + 4)/2) + 2)*(2*re(n) + 1)/(pi*((2*re(n) + 1)^2 + 4*im(n)^2)) + i*(-2*(((-pi^2*(3*re(n)^2*im(n) - im(n)^3) - 4*pi^2*(4*re(n)^3*im(n) - 4*re(n)*im(n)^3) - 4*pi^2*(5*re(n)^4*im(n) - 10*re(n)^2*im(n)^3 + im(n)^5))^2 + (-pi^2*(re(n)^3 - 3*re(n)*im(n)^2) - 4*pi^2*(re(n)^4 - 6*re(n)^2*im(n)^2 + im(n)^4) - 4*pi^2*(re(n)^5 - 10*re(n)^3*im(n)^2 + 5*re(n)*im(n)^4) + 4)^2)^(1/4)*cos(atan2(-pi^2*(3*re(n)^2*im(n) - im(n)^3) - 4*pi^2*(4*re(n)^3*im(n) - 4*re(n)*im(n)^3) - 4*pi^2*(5*re(n)^4*im(n) - 10*re(n)^2*im(n)^3 + im(n)^5), -pi^2*(re(n)^3 - 3*re(n)*im(n)^2) - 4*pi^2*(re(n)^4 - 6*re(n)^2*im(n)^2 + im(n)^4) - 4*pi^2*(re(n)^5 - 10*re(n)^3*im(n)^2 + 5*re(n)*im(n)^4) + 4)/2) + 2)*im(n)/(pi*((2*re(n) + 1)^2 + 4*im(n)^2)) + ((-pi^2*(3*re(n)^2*im(n) - im(n)^3) - 4*pi^2*(4*re(n)^3*im(n) - 4*re(n)*im(n)^3) - 4*pi^2*(5*re(n)^4*im(n) - 10*re(n)^2*im(n)^3 + im(n)^5))^2 + (-pi^2*(re(n)^3 - 3*re(n)*im(n)^2) - 4*pi^2*(re(n)^4 - 6*re(n)^2*im(n)^2 + im(n)^4) - 4*pi^2*(re(n)^5 - 10*re(n)^3*im(n)^2 + 5*re(n)*im(n)^4) + 4)^2)^(1/4)*(2*re(n) + 1)*sin(atan2(-pi^2*(3*re(n)^2*im(n) - im(n)^3) - 4*pi^2*(4*re(n)^3*im(n) - 4*re(n)*im(n)^3) - 4*pi^2*(5*re(n)^4*im(n) - 10*re(n)^2*im(n)^3 + im(n)^5), -pi^2*(re(n)^3 - 3*re(n)*im(n)^2) - 4*pi^2*(re(n)^4 - 6*re(n)^2*im(n)^2 + im(n)^4) - 4*pi^2*(re(n)^5 - 10*re(n)^3*im(n)^2 + 5*re(n)*im(n)^4) + 4)/2)/(pi*((2*re(n) + 1)^2 + 4*im(n)^2))) + 2*((-pi^2*(3*re(n)^2*im(n) - im(n)^3) - 4*pi^2*(4*re(n)^3*im(n) - 4*re(n)*im(n)^3) - 4*pi^2*(5*re(n)^4*im(n) - 10*re(n)^2*im(n)^3 + im(n)^5))^2 + (-pi^2*(re(n)^3 - 3*re(n)*im(n)^2) - 4*pi^2*(re(n)^4 - 6*re(n)^2*im(n)^2 + im(n)^4) - 4*pi^2*(re(n)^5 - 10*re(n)^3*im(n)^2 + 5*re(n)*im(n)^4) + 4)^2)^(1/4)*sin(atan2(-pi^2*(3*re(n)^2*im(n) - im(n)^3) - 4*pi^2*(4*re(n)^3*im(n) - 4*re(n)*im(n)^3) - 4*pi^2*(5*re(n)^4*im(n) - 10*re(n)^2*im(n)^3 + im(n)^5), -pi^2*(re(n)^3 - 3*re(n)*im(n)^2) - 4*pi^2*(re(n)^4 - 6*re(n)^2*im(n)^2 + im(n)^4) - 4*pi^2*(re(n)^5 - 10*re(n)^3*im(n)^2 + 5*re(n)*im(n)^4) + 4)/2)*im(n)/(pi*((2*re(n) + 1)^2 + 4*im(n)^2)))