How do you solve #x^ { 3} - x ^ { 2} - 11x + 11= 0#?

1 Answer
Tamir E.
Nov 19, 2017

#x_1=1#
#x_2=sqrt11#
#x_3=-sqrt11#

Explanation:

#x^3-x^2-11x+11=0#
#=> x^2(x-1)-11(x-1)=0#

let #x-1=t#
#=> x^2(t)-11(t)=0#
#=> (x^2-11)(t)=0#

#=> (x^2-11)(x-1)=0#

So:
#(x-1)=0 => x=1#
OR
#(x^2-11)=0 => x=+-sqrt(11)#

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