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:

$x^3-3x^2-4=\frac{1}{x-1}+5$

this is equivalent to:

$x^3-3x^2=\frac{1}{x-1}+5+4$

that is:

$x^3-3x^2=\frac{1}{x-1}+9$

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

$x\approx\: 3.68875$