`=>` Tặng bạn
`c)`
$\(\left(x+4\right)^4+\left(x+6\right)^4=82\)$
`Đặt a = x + 5`
`Ta có:`
$\(\left(x+4\right)^4+\left(x+6\right)^4=82\)$
$\(\Leftrightarrow\left(a-1\right)^4+\left(a+1\right)^4\)$
$\(\Leftrightarrow\left[\left(a-1\right)^2\right]^2+\left[\left(a+1\right)^2\right]^2=82\)$
$\(\Leftrightarrow\left(a^2-2a+1\right)^2+\left(a+2a+1\right)^2=82\)$
$\(\Leftrightarrow\left(a^2+1\right)^2-4a\left(a^2+1\right)+4a^2+\left(a^2+1\right)^2+4a\left(a^2+a\right)+4a^2=82\) \(\Leftrightarrow\left(a^2+1\right)^2+4a^2=41\)$
$\(\Leftrightarrow a^4+6a^2+1=41\)$
$\(\Leftrightarrow a^4+6a^2-40a=0\)$
$\(\Leftrightarrow\left[{}\begin{matrix}a^2=-10\left(loại\right)\\a^2=4\end{matrix}\right.\)$
$\(\Leftrightarrow\left[{}\begin{matrix}a=2\\a=-2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=-7\end{matrix}\right.\)$
`a)b)`
`=>` Bạn xem hình
