Question

ПОЖАЛУЙСТА ПОМОГИТЕ!​

Answer 1

$\displaystyle\bf\\(x^{2} -4x+1)(x^{2} -4x-3)=12$

Сделаем замену :

$\displaystyle\bf\\x^{2} -4x-1=m \ \ \ \ \Rightarrow \ \ \ x^{2} -4x+1=m+2 \ \ \ \ \Rightarrow \ \ \ x^{2} -4x-3=m-2\\\\\\(m+2)(m-2)=12\\\\m^{2} -4=12\\\\m^{2} =16\\\\m_{1,2} =\pm \ 4\\\\1) \ m=-4\\\\x^{2}-4x-1=-4\\\\x^{2} -4x+3=0\\\\Teorema \ Vieta:\\\\x_{1} + x_{2} =4\\\\x_{1} \cdot x_{2} =3\\\\x_{1} =1 \ \ , \ \ x_{2} =3\\\\2) \ m=4\\\\x^{2} -4x-1=4\\\\x^{2} -4x-5=0\\\\Teorema \ Vieta:\\\\x_{1} + x_{2} =4\\\\x_{1} \cdot x_{2} =-5$

$\displaystyle\bf\\x_{1} =-1 \ \ , \ \ x_{2} =5\\\\\\1+3+(-1)+5=8\\\\\\Otvet \ : \ 8$

Answer 2

Все запредельно просто

Введем замену x^2-4x+1 = а, тогда

x^2-4x+1 -4 = а - 4

x^2-4x-3 = а - 4

$a(a-4) = 12\\a^{2}-4a - 12 = 0$

по т. Виета

a = 6 или а = -2

x^2-4x-5 = 0 или x^2-4x+3 = 0

x = 5 или х = -1 или х = 3 или х = 1

сумма  8