Question

Consider the equation below.x3 – 3x2 – 4 = 1/x-1+ 5The solutions to the equation are approximately x=and x=

Answer 1

Question:

Solution:

Consider the following equation:

`x^3-3x^2-4=(1)/(x-1)+5`

this is equivalent to:

`x^3-3x^2=(1)/(x-1)+5+4`

that is:

`x^3-3x^2=(1)/(x-1)+9`

Multiplying both sides by (x-1), we obtain:

`(x-1)(x^3-3x^2)=1+9(x-1)`

this is equivalent to:

`(x-1)x^3-3x^2(x-1)=1+9(x-1)`

solving for x, we obtain that the correct solutions are:

`x\text{ }\approx0.90672`

and

`x\approx\: 3.68875`