Question

Знайти х:
(x+3)**4+(x+1)**4=16
4 это степень

Answer 1

$\displaystyle\bf\\(x+3)^{4} +(x+1)^{4} =16\\\\x+2=m \ \ \Rightarrow \ \ x=m-2 \ \ \Rightarrow \ \ x+3=m+1 \ \ \Rightarrow \ \ x+1=m-1\\\\(m+1)^{4} +(m-1)^{4} =16\\\\m^4-4m^3+6m^2-4m+1+m^4+4m^3+6m^2+4m+1-16=0\\\\2m^4+12m^2-14=0\\\\m^4+6m^2-7=0\\\\Teorema \ Vieta \ :\\\\m_{1}^{2} +m_{2} ^{2} = -6\\\\m_{1}^{2} \cdot m_{2} ^{2} =-7\\\\m_{1} ^{2} =1\\\\m_{2} ^{2} =-7 < 0 \ - \ ne \ podxodit\\\\\left[\begin{array}{ccc}m=-1\\m=1\end{array}\right$

$\displaystyle\bf\\1)\\\\x+2=-1 \ \ \ \Rightarrow \ \ \ x_{1} =-3\\\\2)\\\\x+2=1 \ \ \ \Rightarrow \ \ \ x_{1} =-1\\\\Otvet \ : \ -1 \ ; \ -3$