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Algebra Level 2

How many distinct x x satisfy this equation? ( x − 1 ) ( x − 1 ) ( x − 1 ) = ( x − 1 ) ( x -1 )( x - 1) ( x -1 ) = ( x -1 )

3 2 1

Refaat M. Sayed by Refaat M. Sayed , 24, Egypt

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2 solutions

Refaat M. Sayed
Sep 2, 2015

We can write this equation like : ( x − 1 ) 3 − ( x − 1 ) = 0 (x-1)^{3} - (x-1) = 0 ( x − 1 ) [ ( x − 1 ) 2 − 1 ] = 0 (x -1) [ ( x - 1)^{2}-1 ] = 0 ( x − 1 ) ( x − 1 − 1 ) ( x − 1 + 1 ) = 0 ( x -1 )( x -1-1 ) ( x -1 + 1) = 0 Then x = 1 & 2 & 0 x =\boxed { 1 \& 2 \& 0} That there are 3 values of x satisfy this equation

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Arulx Z
Sep 4, 2015

Little rearranging shows that the degree of the equation is 3. Therefore by Fundamental Theorem of Algebra, it has 3 not necessarily distinct roots.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Thanks. I've edited the problem to make this less trivial.

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