127.sagews

4.1. $x^2 1 = 0$.

solve(x^2-1==0,x)

[x == -1, x == 1]

solve(x^2-1,x)

[x == -1, x == 1]

(x^2-1).solve(x)

[x == -1, x == 1]

4.2. $x^3 + 2x^2 - 4x - 5 = 0$.

solve(x^3+2*x^2-4*x-5,x)

[x == (-sqrt(21) - 1)/2, x == (sqrt(21) - 1)/2, x == -1]

4.3. br> $\left\{ \begin{array}{ll} x^3+y^3=19\\ {x^2}{y}+{x}{y^2}=-6 \text{.} \end{array} \right.$

x,y=var('x,y')
solve([x^3+y^3==19,x^2*y+x*y^2==-6],x,y)

[[x == -2, y == 3], [x == 3, y == -2]]

4.4. $\sin{x}-{x}-\frac{π}{2}=0$

eq=sin(x)-x-pi/2
solve(eq==0)

\left[x = \frac{{2 \sin \left( x \right)} - \pi}{2}\right]

4.5. $\sin{x}-{x}-\frac{π}{2}=0$

plot(eq,-10,10)

find_root(eq,-5,0)

-2.309881460010057

4.6. $|x-3|-3=0$

solve(abs(x-3)-4,x)

[abs(x - 3) == 4]

plot(abs(x-3)-4,-10,10)

find_root(abs(x-3)-4,-2.5,0)

-1.0

4.7. $2^{4x}-5{2^x}-3 = 0$.

f=2^(4*x)-5*2^x+3
plot(f,-5,1)

print 'x1=',find_root(f,-1,0)
print 'x2=', find_root(f,0,1)

x1= -0.662266966896 x2= 0.511202342796