1604.sagews

solve(x^2-2*x+1/5,x)

[x == -2/5*sqrt(5) + 1, x == 2/5*sqrt(5) + 1]

RR(-2/5*sqrt(5) + 1); RR(2/5*sqrt(5) + 1)

0.105572809000084 1.89442719099992

RR(1/tan(2*pi/5)^2); RR(1/tan(pi/5)^2)

0.105572809000084 1.89442719099992

solve(x^4-(28/3)*x^3+14*x^2-4*x+1/9,x)

[x == -1/2*(I*sqrt(3) + 1)*(32/9*I*sqrt(3) + 32/3)^(1/3) + 1/3*(8*I*sqrt(3) - 8)/(32/9*I*sqrt(3) + 32/3)^(1/3) + 3, x == -1/2*(-I*sqrt(3) + 1)*(32/9*I*sqrt(3) + 32/3)^(1/3) + 1/3*(-8*I*sqrt(3) - 8)/(32/9*I*sqrt(3) + 32/3)^(1/3) + 3, x == (32/9*I*sqrt(3) + 32/3)^(1/3) + 16/3/(32/9*I*sqrt(3) + 32/3)^(1/3) + 3, x == (1/3)]

x1 =CC(-1/2*(I*sqrt(3) + 1)*(32/9*I*sqrt(3) + 32/3)^(1/3) +1/3*(8*I*sqrt(3) - 8)/(32/9*I*sqrt(3) + 32/3)^(1/3) + 3);x2=CC(-1/2*(-I*sqrt(3) + 1)*(32/9*I*sqrt(3) + 32/3)^(1/3) + 1/3*(-8*I*sqrt(3)- 8)/(32/9*I*sqrt(3) + 32/3)^(1/3) + 3);x3=CC((32/9*I*sqrt(3) + 32/3)^(1/3) + 16/3/(32/9*I*sqrt(3) + 32/3)^(1/3) + 3);x4=CC(1/3)

x1;x2;x3;x4

1.42027662546121 0.0310912041257634 7.54863217041303 + 5.55111512312578e-17*I 0.333333333333333

RR(1/tan(4*pi/9)^2);RR(1/tan(3*pi/9)^2);RR(1/tan(2*pi/9)^2);RR(1/tan(pi/9)^2)

0.0310912041257634 0.333333333333333 1.42027662546121 7.54863217041303