CSH 6.3 Predicates MrG 2012.0208

2967 days ago by CSH2012

#2) (x-1)^2>=4 solve((x-1)^2>=4,x) 
       
[[x <= -1], [x >= 3]]
[[x <= -1], [x >= 3]]
equ=(x-1)^2>=4;show(equ) equ=(equ).expand();show(equ) equ=equ-4;show(equ) equ=equ.lhs().factor();show(equ) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x - 1\right)}^{2} \geq 4
\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} - 2 \, x + 1 \geq 4
\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} - 2 \, x - 3 \geq 0
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x - 3\right)} {\left(x + 1\right)}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x - 1\right)}^{2} \geq 4
\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} - 2 \, x + 1 \geq 4
\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} - 2 \, x - 3 \geq 0
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x - 3\right)} {\left(x + 1\right)}
#3) x^2+y^2=1 var('y') solve(x^2+y^2==1,y) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[y = -\sqrt{-x^{2} + 1}, y = \sqrt{-x^{2} + 1}\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[y = -\sqrt{-x^{2} + 1}, y = \sqrt{-x^{2} + 1}\right]
plot(sqrt(-x^2+1),xmin=0,xmax=1,aspect_ratio=1,fill=true,fillcolor='orange') 
       
#4a) (x-2)(y-1)==0: x=2, y=1 
       
#4b) (x-2)(y-1)>0: (x>2 and y>1) or (x<2 and y<1)