Question

\((x+2)^{4}+(x+8)^{4}=272\)

Answer 1

l8 học đặt r đk 

đặt  t=x+5

=>pt: 

\(\left(t-3\right)^4+\left(t+3\right)^4=272\\ \Leftrightarrow t^4-4t^3+54t^2-108t+81+t^4+4t^3+54t^2+108t+81=271\\ \Leftrightarrow2t^4+108t^2-110=0\\ \Leftrightarrow\left(t^2-1\right)\left(2t^2+110\right)=0\\ \Leftrightarrow t^2=1\)

( 2t^2 +110 > 0 mọi x)

\(\Leftrightarrow\left[{}\begin{matrix}t=1\Rightarrow x=-4\\t=-1\Rightarrow x=-6\end{matrix}\right.\)