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saul85 [17]
2 years ago
9

The equation x^3-5x=59 has a solution between 4 and 5. Use a trial and improvement method to find this solution. Give your answe

r to one decimal place. You must show all your working. On the same line as your final answer, you must write to "1 decimal place".
Mathematics
1 answer:
vodomira [7]2 years ago
6 0

Answer:

The answer is "4.3".

Step-by-step explanation:

Given:

\to x^3 - 5x - 59 = 0

When x = 4.1:  

\to f(4.1) = (4.1)^3 - 5(4.1) - 59 = -10.579

When x= 4.2:

f(4.2) = 4.2^3 - 5(4.2) - 59 = -5.912

When x = 4.3:

\to f(4.3) = -0.993 (closer to 0)

\to f(4.4) = 4.184

  • It changes the sign so, the root lies in 4.3 and 4.4.

When x = 4.35:

\to f(4.35) = 1.563

When the root is closer to 4.3 than 4.4 So, 1.563 is closer to zero than 4.184.

When x = 4.32:

\to f(4.32) = 0.0216 close to zero.

So the answer is 4.3 to 1 decimal place.  

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Center = (4, 7)

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===========================================================

Explanation:

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see the attached figure to better understand the problem

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