Đặt \(x+2=t\)
\(\Rightarrow\left(x+1\right)^4+\left(x+3\right)^4=82\)
\(\Leftrightarrow\left(t-1\right)^4+\left(t+1\right)^4=82\)
\(\Leftrightarrow\left[\left(t-1\right)^2\right]^2+\left[\left(t+1\right)^2\right]^2=82\)
\(\Leftrightarrow\left(t^2-2t+1\right)^2+\left(t+2t+1\right)^2=82\)
\(\Leftrightarrow\left(t^2+1\right)^2-4t\left(t^2+1\right)+4t^2+\left(t^2+1\right)^2+4t\left(t^2+1\right)+4t^2=82\)
\(\Leftrightarrow\left(t^2+1\right)^2+4t^2=41\)
\(\Leftrightarrow t^4+6t^2+1=41\)
\(\Leftrightarrow t^4+6t^2-40t=0\)
\(\Leftrightarrow\left[\begin{matrix}t^2=-10\left(lo\text{ại}\right)\\t^2=4\Rightarrow\left[\begin{matrix}t=2\\t=-2\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[\begin{matrix}x=0\\x=-4\end{matrix}\right.\)
x=0 hoat 4 nha bn
chuc bn hoc tot
happy new year