CM 1.0 Algebra MrG 2011.0909

3737 days ago by calcpage123

Algebra!

factor(2*x^2+4*x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, {\left(x + 2\right)} x
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, {\left(x + 2\right)} x
solve(2*x^2+4*x==0,x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \left(-2\right), x = 0\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \left(-2\right), x = 0\right]
factor(x^2-9) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x - 3\right)} {\left(x + 3\right)}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x - 3\right)} {\left(x + 3\right)}
solve(x^2-9==0,x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \left(-3\right), x = 3\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \left(-3\right), x = 3\right]
factor(x**2+2*x+1) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x + 1\right)}^{2}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x + 1\right)}^{2}
solve(x**2+2*x+1==0,x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \left(-1\right)\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \left(-1\right)\right]
factor(x**2+2*x+2) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} + 2 \, x + 2
\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} + 2 \, x + 2
solve(x**2+2*x+2==0,x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \left(-i - 1\right), x = \left(i - 1\right)\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \left(-i - 1\right), x = \left(i - 1\right)\right]
factor(x**2+2*x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x + 2\right)} x
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x + 2\right)} x
factor(x**2+2*x-1) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} + 2 \, x - 1
\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} + 2 \, x - 1
solve(x**2+2*x-1==0,x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = -\sqrt{2} - 1, x = \sqrt{2} - 1\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = -\sqrt{2} - 1, x = \sqrt{2} - 1\right]
a=plot(x^2+2*x+2,xmin=-4,xmax=2,color='red') b=plot(x^2+2*x+1,xmin=-4,xmax=2,color='green') c=plot(x^2+2*x+0,xmin=-4,xmax=2,color='orange') d=plot(x^2+2*x-1,xmin=-4,xmax=2) a+b+c+d 
       
factor(125*x^3+64) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(5 \, x + 4\right)} {\left(25 \, x^{2} - 20 \, x + 16\right)}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(5 \, x + 4\right)} {\left(25 \, x^{2} - 20 \, x + 16\right)}
expand((5*x+4)*(25*x^2-20*x+16)) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}125 \, x^{3} + 64
\newcommand{\Bold}[1]{\mathbf{#1}}125 \, x^{3} + 64
factor(27*x^9-8) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(3 \, x^{3} - 2\right)} {\left(9 \, x^{6} + 6 \, x^{3} + 4\right)}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(3 \, x^{3} - 2\right)} {\left(9 \, x^{6} + 6 \, x^{3} + 4\right)}
expand((3*x^3-2)*(9*x^6+6*x^3+4)) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}27 \, x^{9} - 8
\newcommand{\Bold}[1]{\mathbf{#1}}27 \, x^{9} - 8
solve(27*x^9-8==0,x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \frac{1}{3} \, 2^{\left(\frac{1}{3}\right)} 3^{\left(\frac{2}{3}\right)} e^{\left(\frac{2}{9} i \, \pi\right)}, x = \frac{1}{3} \, 2^{\left(\frac{1}{3}\right)} 3^{\left(\frac{2}{3}\right)} e^{\left(\frac{4}{9} i \, \pi\right)}, x = \frac{1}{6} \, {\left(i \, 2^{\left(\frac{1}{3}\right)} \sqrt{3} - 2^{\left(\frac{1}{3}\right)}\right)} 3^{\left(\frac{2}{3}\right)}, x = \frac{1}{3} \, 2^{\left(\frac{1}{3}\right)} 3^{\left(\frac{2}{3}\right)} e^{\left(\frac{8}{9} i \, \pi\right)}, x = \frac{1}{3} \, 2^{\left(\frac{1}{3}\right)} 3^{\left(\frac{2}{3}\right)} e^{\left(-\frac{8}{9} i \, \pi\right)}, x = \frac{1}{6} \, {\left(-i \, 2^{\left(\frac{1}{3}\right)} \sqrt{3} - 2^{\left(\frac{1}{3}\right)}\right)} 3^{\left(\frac{2}{3}\right)}, x = \frac{1}{3} \, 2^{\left(\frac{1}{3}\right)} 3^{\left(\frac{2}{3}\right)} e^{\left(-\frac{4}{9} i \, \pi\right)}, x = \frac{1}{3} \, 2^{\left(\frac{1}{3}\right)} 3^{\left(\frac{2}{3}\right)} e^{\left(-\frac{2}{9} i \, \pi\right)}, x = \frac{1}{3} \, 2^{\left(\frac{1}{3}\right)} 3^{\left(\frac{2}{3}\right)}\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \frac{1}{3} \, 2^{\left(\frac{1}{3}\right)} 3^{\left(\frac{2}{3}\right)} e^{\left(\frac{2}{9} i \, \pi\right)}, x = \frac{1}{3} \, 2^{\left(\frac{1}{3}\right)} 3^{\left(\frac{2}{3}\right)} e^{\left(\frac{4}{9} i \, \pi\right)}, x = \frac{1}{6} \, {\left(i \, 2^{\left(\frac{1}{3}\right)} \sqrt{3} - 2^{\left(\frac{1}{3}\right)}\right)} 3^{\left(\frac{2}{3}\right)}, x = \frac{1}{3} \, 2^{\left(\frac{1}{3}\right)} 3^{\left(\frac{2}{3}\right)} e^{\left(\frac{8}{9} i \, \pi\right)}, x = \frac{1}{3} \, 2^{\left(\frac{1}{3}\right)} 3^{\left(\frac{2}{3}\right)} e^{\left(-\frac{8}{9} i \, \pi\right)}, x = \frac{1}{6} \, {\left(-i \, 2^{\left(\frac{1}{3}\right)} \sqrt{3} - 2^{\left(\frac{1}{3}\right)}\right)} 3^{\left(\frac{2}{3}\right)}, x = \frac{1}{3} \, 2^{\left(\frac{1}{3}\right)} 3^{\left(\frac{2}{3}\right)} e^{\left(-\frac{4}{9} i \, \pi\right)}, x = \frac{1}{3} \, 2^{\left(\frac{1}{3}\right)} 3^{\left(\frac{2}{3}\right)} e^{\left(-\frac{2}{9} i \, \pi\right)}, x = \frac{1}{3} \, 2^{\left(\frac{1}{3}\right)} 3^{\left(\frac{2}{3}\right)}\right]
l=solve(8*x^9-27==0,x) for i in [0..8]: l[i].rhs().n(digits=3) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}0.877 + 0.736i
\newcommand{\Bold}[1]{\mathbf{#1}}0.199 + 1.13i
\newcommand{\Bold}[1]{\mathbf{#1}}-0.572 + 0.991i
\newcommand{\Bold}[1]{\mathbf{#1}}-1.08 + 0.391i
\newcommand{\Bold}[1]{\mathbf{#1}}-1.08 - 0.391i
\newcommand{\Bold}[1]{\mathbf{#1}}-0.572 - 0.991i
\newcommand{\Bold}[1]{\mathbf{#1}}0.199 - 1.13i
\newcommand{\Bold}[1]{\mathbf{#1}}0.877 - 0.736i
\newcommand{\Bold}[1]{\mathbf{#1}}1.14
\newcommand{\Bold}[1]{\mathbf{#1}}0.877 + 0.736i
\newcommand{\Bold}[1]{\mathbf{#1}}0.199 + 1.13i
\newcommand{\Bold}[1]{\mathbf{#1}}-0.572 + 0.991i
\newcommand{\Bold}[1]{\mathbf{#1}}-1.08 + 0.391i
\newcommand{\Bold}[1]{\mathbf{#1}}-1.08 - 0.391i
\newcommand{\Bold}[1]{\mathbf{#1}}-0.572 - 0.991i
\newcommand{\Bold}[1]{\mathbf{#1}}0.199 - 1.13i
\newcommand{\Bold}[1]{\mathbf{#1}}0.877 - 0.736i
\newcommand{\Bold}[1]{\mathbf{#1}}1.14
plot(8*x^9-27,xmax=1.2)