233.sagews

var('p,xmax,a,x,lfmax')

(p, xmax, a, x, lfmax)

solve(1*1/3*sqrt(-6+3*e**(12*(x-a))+3*e**(-12*(x-a))-432*(x-a)**2)-(-1*1/3*sqrt(-6+3*e**(12*(x+a))+3*e**(-12*(x+a))-432*(x+a)**2))==5,x)

[]

p=1*1/3*sqrt(-6+3*e**(12*(x-a))+3*e**(-12*(x-a))-432*(x-a)**2)-(-1*1/3*sqrt(-6+3*e**(12*(x+a))+3*e**(-12*(x+a))-432*(x+a)**2))

q=simplify(p)

solve(p**2-25==0,x)

[x^2 == (2*e^(12*x)*sqrt(3*e^(24*(x - a)) + (-432*x^2 + 864*a*x - 432*a^2 - 6)*e^(12*(x - a)) + 3)*sqrt(3*e^(24*(x + a)) + (-432*x^2 - 864*a*x - 432*a^2 - 6)*e^(12*(x + a)) + 3) + (3*e^(24*(x - a)) + (-864*a^2 - 237)*e^(12*(x - a)) + 3)*e^(12*(x + a)) + 3*e^(12*(x - a)) + 3*e^(36*x + 12*a))*e^(-12*(x + a) - 12*(x - a))/864, e^(-(24*x)) == 0]

solve(p(a=0.01)==lfmax,x)

[]

q(a=0.01).plot(0,0.5)

solve(sin(x)^2==0.66,x)

[x == -arcsin(sqrt(33)/(5*sqrt(2))), x == arcsin(sqrt(33)/(5*sqrt(2)))]