Answer:
Step-by-step explanation:
[tex]20-x^3-7x^2=0[/tex]
a)
- Add [tex]x^3[/tex] to both sides of the equation: [tex]20-7x^2=x^3[/tex]
- Divide both sides by [tex]x^2[/tex]: [tex]\frac{20}{x^2} -\frac{7x^2}{x^2} =\frac{x^3}{x^2}[/tex] ⇒ [tex]\frac{20}{x^2} -7 =x[/tex]
b)
[tex]x_1=\frac{20}{(x_0)^2} -7[/tex]
⇒ [tex]x_1=\frac{20}{(-9)^2} -7[/tex]
⇒ [tex]x_1=-\frac{547}{81}[/tex]
[tex]x_2=\frac{20}{(x_1)^2} -7[/tex]
⇒ [tex]x_2=\frac{20}{(-\frac{547}{81})^2} -7[/tex]
⇒ [tex]x_2=-6.561443673...[/tex]
[tex]x_3=\frac{20}{(x_2)^2} -7[/tex]
⇒ [tex]x_3=\frac{20}{(-6.561443673...)^2} -7[/tex]
⇒ [tex]x_3=-6.535451368...[/tex]
c) approximation to the location of one of the roots of the equation. Each iteration gives a slightly more accurate value of a root [tex]x[/tex].
