Using maxima for high school mathematics



On 3/04/2011 3:51 PM, Daniel Dalton wrote:
> 4) Finally, I'm having trouble solving some more complicated equations
> with maxima. According to my text book there is real solutions. How can
> I find the real solution for the below equation? Input/output is
> below. (Note, I'm not familiar with complex numbers.)
Hi Dan,

There are at least two ways to attack 4)

1. Float isn't always sufficient with complex numbers.  Try 
rectform(float(expression))).  You are left with a small imaginary part 
due to rounding errors.

2. Use the realroots() function to extract the real roots.  It returns 
rational approximations to the real solution, which can be converted to 
floating point using float().  Try realroots(x^2-2=0).  Do you 
understand that maxima approximating the irrational number sqrt(2)?

(%i1) display2d:false;
(%o1) false
(%i2) expr:x^3-17*x^2-56*x+1153=0;
(%o2) x^3-17*x^2-56*x+1153 = 0
(%i3) rectform(float(solve(expr,x)));
(%o3) [x = 1.7763568394002505E-15*%i+9.008409308902849,
        x = -8.8817841970012523E-16*%i-8.002450376978054,
        x = 15.99404106807521-8.8817841970012523E-16*%i]
(%i4) realroots(expr);
(%o4) [x = -268517677/33554432,x = 302272057/33554432,x = 
536670963/33554432]
(%i5) float(%);
(%o5) [x = -8.002450376749039,x = 9.008409291505814,x = 15.9940410554409]

     David