Question 1121373
 {{{x= 12-sqrt(12-sqrt(x))}}}

 {{{x- 12=sqrt(12-sqrt(x))}}} .......square both sides

 {{{(x- 12)^2=(sqrt(12-sqrt(x)))^2}}}

 {{{x^2- 24x+144= 12-sqrt(x)}}}

{{{x^2- 24x+144-12= -sqrt(x)}}}

{{{x^2- 24x+132= -sqrt(x)}}} .....square both sides

{{{(x^2- 24x+132)^2= (-sqrt(x) )^2}}}

{{{x^4 - 48 x^3 + 840 x^2 - 6336 x + 17424=x}}}

x^4 - 48 x^3 + 840 x^2 - 6336 x-x + 17424=0

{{{x^4 - 48 x^3 + 840 x^2 - 6337 x + 17424=0}}}

solutions:

{{{x=9}}}

{{{x=16}}}

{{{x=(23+3sqrt(5))/2}}}

{{{x=(23-3sqrt(5))/2}}}


if you verify solutions, you will notice that  only {{{x=9}}} will make {{{ x= 12-sqrt(12-sqrt(x))}}} true