$e) \sqrt[4]{47 - 2x} + \sqrt[4]{35 + 2x} = 4$
`text{Đặt}`
\(\left\{ \begin{array}{l}\sqrt[4]{47 - 2x} = a\\\sqrt[4]{35 + 2x} = b\end{array} \right.\)
`-> a^4 + b^4 = 82` `(1)`
`text{Phương trình đã cho trở thành}`
`a + b = 4`
`(1)`
`-> a^4 + 2a^{2}b^{2} + b^4 - 2a^{2}b^{2} = 82`
`-> (a^2 + b^2)^2 - 2a^{2}b^{2} = 82`
`-> (a^2 + 2ab + b^2 - 2ab)^{2} - 2a^{2}b^{2} = 82`
`-> [(a + b)^2 - 2ab]^2 - 2a^{2}b^{2} = 82`
`-> (4^2 - 2ab)^2 - 2(ab)^2 = 82`
`-> 256 - 64ab + 4(ab)^2 - 2(ab)^2 - 82 = 0`
`-> 2(ab)^2 - 64b + 174 = 0`
`->` \(\left[ \begin{array}{l}ab = 29\\ab = 3\end{array} \right.\)
`text{Do}` `a + b = 4`
`-> a.b <= 4`
`-> (a, b) = {(3; 1); (1; 3)}`
`->` \(\left[ \begin{array}{l}\left[ \begin{array}{l}\sqrt[4]{47 - 2x} = 3\\\sqrt[4]{35 + 2x} = 1\end{array} \right.\\\left[ \begin{array}{l}\sqrt[4]{47 - 2x} = 1\\\sqrt[4]{35 + 2x} = 3\end{array} \right.\end{array} \right.\)
`->` \(\left[ \begin{array}{l}x=-17\\x=23\end{array} \right.\)
`-> S = {-17; 23}`
