Question

The equation x^3 - 6x = 72 has a solution between 4 and 5.

Answer 1

Answer:

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