Question

the equation x^3-3x=1 has a solution between 1.8 and 1.9. use a trial and improvement method to find this solution. give your answer correct to 2 decimal places.

Answer 1

Explanation:

1.8=-0.568 is too small

1.9=0.159 is too big

1.87=-0.70797 is too small

1.88=0.004672 is too big

Next, I plugged in 1.87 to get the answer closer to 1:

1.87^3-3*1.87=0.93

Finally, I plugged in 1.88 to get even closer to 1:

1.88^3-3*1.88=1.00

1.875=-0.033203125 is too small

so it should be 1.88 to 2 decimal places

hope this helped :)

Answer 2

The solution to the equation x³ - 3x = 1 is given as :

1.88

Explanation:

In the above question, we are given the equation

x³ - 3x = 1 ... Equation 1

and we are told the answer lies between 1.8 - 1.9

Using the trial and improvement method approximating to 2 decimal places

a. First trial we use 1.84 for x in equation 1

1.84³ - 3×1.84 = 0.71

This first trial using 1.84 too small

b. Second trial we use 1.86 for x in equation 1

1.86³ - 3×1.86 = 0.86

This second trial using 1.86 as well is too small

c. For our third trial we use 1.89 for x in equation 1

1.89³ - 3×1.89 = 1.08

This third trial using 1.89 is large. Our target is 1.00

d. Our fourth trial we use 1.88 for x in equation 1

1.88³ - 3×1.88 = 1.004

Approximately to 2 decimal places.

We have = 1.00

Hence the solution to the equation

x³ - 3x = 1 after using the trial and improvement method is 1.88