Bài 1. Ta có:
\( a = \root 3 \of {{5^3}} + \root 3 \of {{{\left( { - 7} \right)}^3}} - 2\root 3 \of {{4^3}} \)\(\,+ {1 \over 3}\root 3 \of {{3^3}{{.2}^3}} \)
\(= 5 + \left( { - 7} \right) - 2.4 + {3 \over 3}.2 = - 8 \)
Bài 2. Ta có:
\(\eqalign{ & \root 3 \of {2x + 1} - 5 = 0 \Leftrightarrow \root 3 \of {2x + 1} = 5 \cr & \Leftrightarrow 2x + 1 = {5^3} \Leftrightarrow 2x + 1 = 125 \cr & \Leftrightarrow x = 62 \cr} \)
Bài 3. Ta có: \(3 > \root 3 \of {25} \Leftrightarrow {3^3} > {\left( {\root 3 \of {25} } \right)^3} \Leftrightarrow 27 > 25\) (luôn đúng)
Bài 4. Ta có:
\(\eqalign{ & \root 3 \of {x - 1} > 2 \Leftrightarrow {\left( {\root 3 \of {x - 1} } \right)^3} > {2^3} \cr & \Leftrightarrow 2x - 1 > 8 \Leftrightarrow x > {9 \over 2} \cr} \)
