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olga55 [171]
3 years ago
9

A) Show that the equation 20-x^3-7x^2=0 can be rearranged to give x=20/x^2 - 7

Mathematics
1 answer:
AVprozaik [17]3 years ago
4 0

Answer:

Step-by-step explanation:

      20-x^3-7x^2=0

a)

  • Add x^3 to both sides of the equation:     20-7x^2=x^3
  • Divide both sides by x^2:    \frac{20}{x^2} -\frac{7x^2}{x^2} =\frac{x^3}{x^2}  ⇒  \frac{20}{x^2} -7 =x

b)

    x_1=\frac{20}{(x_0)^2} -7

⇒ x_1=\frac{20}{(-9)^2} -7

⇒ x_1=-\frac{547}{81}

    x_2=\frac{20}{(x_1)^2} -7

⇒ x_2=\frac{20}{(-\frac{547}{81})^2} -7

⇒ x_2=-6.561443673...

   x_3=\frac{20}{(x_2)^2} -7

⇒ x_3=\frac{20}{(-6.561443673...)^2} -7

⇒ x_3=-6.535451368...

c) approximation to the location of one of the roots of the equation.  Each iteration gives a slightly more accurate value of a root x.

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