SAGE MATH

zad.1.

a)
sage: rownaniee = x + 2 == 3*x - 5
sage: solve(rownaniee, x)

b)
sage: rownanieee = x^2 + 3*x - 1 == 0
sage: solve(rownanieee, x)

c)
sage: rownanieeee = 3^x * (x^2 - 4) == 0
sage: solve(rownanieeee, x)


zad.2.

a)
sage: var('x,y')
sage: solve([5*x + 2*y == 4, x - 4*y == -2],x,y)

P = implicit_plot(5*x + 2*y == 4, (x,-2,2), (y,-2,2), color="red")
G = implicit_plot(x - 4*y == -2, (x,-2,2), (y,-2,2), color="blue")
R = points([(6/11, 7/11)], size=45, color="green", figsize=4)
P + G + R

lub:

show(implicit_plot((5*x+2*y==4), (x,-2,2), (y,-2,2), color="red")\
+ implicit_plot((x-4*y==-2), (x,-2,2), (y,-2,2), color="blue")\
+ points([(6/11, 7/11)], size=45, color="green", figsize=4))


b)
sage: var('x,y')
sage: solve([x^2 + 2*x + y^2 - 4*x == 20, 2*x - y == 0],x,y)

A = implicit_plot(x^2 + 2*x + y^2 - 4*x == 20, (x,-10,10), (y,-10,10), color="red")
B = implicit_plot(2*x - y == 0, (x,-10,10), (y,-10,10), color="blue")
C = points([(-1/5*sqrt(101) + 1/5,-2/5*sqrt(101) + 2/5),(1/5*sqrt(101) + 1/5,2/5*sqrt(101) + 2/5)], size=45, color="green",figsize=4)
A+B+C