The equation x^3 - 6x = 72 has a solution between 4 and 5. Use a trial and improvement method to find the solution correct to one decimal place,

By using the trial and improvement method the solution of the equation ( - 6x = 72) is 4.64 and this can be determined by using the given data.

Given :

The equation ( - 6x = 72) has a solution between 4 and 5.

There are ten possible solutions according to the trial and improvement method that is (4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 5).

First, check the value of the function at the end terms of the above interval.

At x = 4.1 the given function becomes:

LHS = 68.921 - 24.6

LHS = 44.321

At x = 5 the given function becomes:

LHS = 125 - 30

LHS = 95

At x = 4.7 the given function becomes:

LHS = 103.823 - 28.2 = 75.623

Now, at x = 4.64 the given function becomes:

LHS = 99.90 - 27.84 = 72.06

LHS RHS

So, by using the trial and improvement method the solution of the equation ( - 6x = 72) is 4.64.

For more information, refer to the link given below:

link

4.6

Step-by-step explanation:

X^3-6x=72

Solution between 4 and 5 correct to one decimal place

This means There are 10 Possible solution (4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 5.0)

Let x=4.1

X^3-6x=72

=4.1^3-6(4.1)

=68.921-24.6

=44.321

This means 4.1 is far from the answer

Let's try a bigger number

Let x=4.8

X^3-6x=72

4.8^3-6(4.8)

=110.592-28.8

=81.792

Let x=4.7

X^3-6x=72

4.7^3-6(4.7)

=103.823-28.2

=75.623

Let x=4.6

X^3-6x=72

4.6^3-6(4.6)

=97.336-27.6

=69.736

It can be said that the solution is between 4.6 and 4.7

Let x=4.62

X^3-6x=72

4.62^3-6(4.62)

=98.611128-27.72

=70.891128

Let x=4.64

X^3-6x=72

4.64^3-6(4.64)

=99.897344-27.84

=72.057344

Let's=4.65

X^3-6x=72

=4.65^3-6(4.65)

=100.544625-27.9

=72.644625

This is greater than 72

We can conclude that the closest answer is 4.64

Let x=4.64

X^3-6x=72

4.64^3-6(4.64)

=99.897344-27.84

=72.057344

Approximately 72

4.64 to one decimal place=4.6

i belive the biggest ratio would be 18: correct me if im wrong