Question

Consider the equation below (in screenshot)

Answer 1

The approximate solution of the equation shown in the picture is x ≈ 39 / 8 (Right choice: B).

How to find an approximate solution of a one-variable equation

The solution of the equation is between x = 4 and x = 5. Now we begin by evaluating each side of the expression (f(x) = x² - 5 · x + 4, g(x) = 2 / (x - 1)) at the average of x = 4 and x = 5.

x = (4 + 5) / 2

x = 4.5

f(4.5) = 4.5² - 5 · 4.5 + 1

f(4.5) = - 5 / 4

g(4.5) = 2 / (4.5 - 1)

g(4.5) = 4 / 7

The solution of the equation is between x = 4.5 and x = 5, then we evaluate at the average:

x = (4.5 + 5) / 2

x = 4.75

f(4.75) = 4.75² - 5 · 4.75 + 1

f(4.75) = - 3 / 16

g(4.75) = 2 / (4.75 - 1)

g(4.75) = 8 / 15

The solution of the equation is between x = 4.75 and x = 5, then we evaluate at the average:

x = (4.75 + 5) / 2

x = 4.875

f(4.875) = 4.875² - 5 · 4.875 + 1

f(4.875) = 25 / 64

g(4.875) = 2 / (4.875 - 1)

g(4.875) = 16 / 31

The approximate solution of the equation shown in the picture is x ≈ 39 / 8 (Right choice: B).

To learn more on successive approximations: brainly.com/question/27191494

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