Question 1197831


{{{9x ^ 4 - 12x ^ 3 + 13x ^ 2 - 12x + 4 = 0}}}.........factor

{{{9x ^ 4 +9x^2- 12x ^ 3- 12x + 4x ^ 2 + 4 = 0}}}

{{{(9x ^ 4 +9x^2)- (12x ^ 3+12x )+ (4x ^ 2 + 4) = 0}}}

{{{9x^2(x ^ 2+1)- 12x(x ^ 2+1 )+ 4(x ^ 2 + 1) = 0}}}

{{{(9 x^2 - 12 x + 4)(x^2 + 1) = 0}}}

{{{(2 - 3x)^2 (x^2 + 1) = 0}}}


solutions:


if {{{(2 - 3x)^2 = 0}}} => {{{(2 - 3x)=0}}}=> {{{2 = 3x}}}=> {{{x = 2/3}}}



if {{{(x^2 + 1) = 0 }}}=> {{{x^2 = -1}}}=>{{{ x= sqrt(-1)}}}=> {{{x= i }}}or {{{x=-i}}}

so,

real solution: 

{{{x = 2/3}}}

complex solutions:

 {{{x = i }}}
{{{ x=-i}}}