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

Sagot :

Question:

Solution:

Consider the following equation:

[tex]x^3-3x^2-4=\frac{1}{x-1}+5[/tex]

this is equivalent to:

[tex]x^3-3x^2=\frac{1}{x-1}+5+4[/tex]

that is:

[tex]x^3-3x^2=\frac{1}{x-1}+9[/tex]

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

[tex](x-1)(x^3-3x^2)=1+9(x-1)[/tex]

this is equivalent to:

[tex](x-1)x^3-3x^2(x-1)=1+9(x-1)[/tex]

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

[tex]x\text{ }\approx0.90672[/tex]

and

[tex]x\approx\: 3.68875[/tex]

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