Question

(x^4 + x^2 + 1)(x^4 + x^2 + 2)=12

Answer 1

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$\displaystyle\bf (x^4+x^2+1)(x^4+x^2+2)=12\\\\(x^4+x^2+1)(x^4+x^2+1+1)=12$

пусть:

$x^4+x^2+1 = t\\t > 0$

$\displaystyle\bf t(t+1)=12\\\\t(t-1)-12=0\\\\t^2+t-12=0\\\\t_1=-4 \ \ \ \ \ t_2 = 3$

$\displaystyle \bf x^4+x^2+1=3\\\\x^4+x^2+1-3=0\\\\x^4+x^2-2=0$

пусть:

$x^2=a\geq 0$

$\displaystyle\bf a^2+a-2=0\\\\a_1=-2 \ \ \ \ \ a_2=1$

$\displaystyle\bf x^2=1\\\\x=\pm1$

ответ: 1 ; -1