Question 984439

Notice that


{{{x^4 + 4x^3 + 6x^2 + 4x + 9}}} = {{{x^4 + 4x^3 + 6x^2 + 4x + 1}}} + {{{8}}} = {{{(x+1)^4}}} + {{{8}}}.


Now,   at  {{{x}}} = {{{sqrt(-2)-1}}}   you have


{{{x+1}}} = {{{sqrt(-2)}}}  and  {{{(x+1)^4}}} = {{{(sqrt(-2))^4}}} = {{{(-2)^2}}} = {{{4}}}.


As a last step, 


{{{x^4 + 4x^3 + 6x^2 + 4x + 9}}} = {{{(x+1)^4}}} + {{{8}}} = {{{4}}} + {{{8}}} = {{{12}}}.


<B>Answer</B>. &nbsp;{{{x^4 + 4x^3 + 6x^2 + 4x + 9}}} = {{{12}}} at {{{x}}} = {{{sqrt(-2)-1}}}.