The unnecessary value

Algebra Level 2

x 3 x 2 x + 1 x 3 x 2 + x 1 = 0 , x = ? \large \frac {x^3 - x^2 - x + 1}{x^3 - x^2 + x- 1} = 0 \qquad , \qquad x = \ ?


The answer is -1.

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2 solutions

Lew Sterling Jr
Apr 3, 2015

Fun Fact:

William Isoroku
Aug 2, 2014

Factor the numerator and denominator by grouping and simplify. Then find the value of x that would make the numerator equal to 0.

You should mention that even though 0 = x 3 x 2 x + 1 = ( x 1 ) 2 ( x + 1 ) 0 = x^3 - x^2 - x + 1 = (x-1)^2(x+1) has a solution x = 1 x = 1 , that is not the solution to the equation because x = 1 x = 1 would make the denominator 0, and hence the expression would be undefined.

Calvin Lin Staff - 6 years, 10 months ago

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I put it that way purposely because I want it to be more than just solving the equation.

William Isoroku - 6 years, 10 months ago

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I meant "mention in your solution". This allows others who were unable to solve the problem, to then learn from your solution.

Your solution is currently too abbreviated. Those who have solved the problem can understand what you are thinking. Those who have not solved the problem, are unable to read your mind to understand how to approach the solution.

Calvin Lin Staff - 6 years, 10 months ago

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