$\begin{array}{l} 2)x = \sqrt[3]{{5\sqrt 2 + 7}} - \sqrt[3]{{5\sqrt 2 - 7}}\\ \Rightarrow {x^3} = 5\sqrt 2 + 7 - \left( {5\sqrt 2 - 7} \right) - 3\sqrt[3]{{25.2 - 49}}.x\\ \Leftrightarrow {x^3} = 14 - 3x\\ \Leftrightarrow {x^3} + 3x - 14 = 0\\ \Leftrightarrow {x^3} - 2{x^2} + 2{x^2} - 4x + 7x - 14 = 0\\ \Leftrightarrow \left( {x - 2} \right)\left( {\underbrace {{x^2} + 2x + 7}_{ > 0}} \right) = 0\\ \Leftrightarrow x = 2\\ 3)x = \sqrt[3]{{20 + 14\sqrt 2 }} - \sqrt[3]{{14\sqrt 2 - 20}}\\ \Leftrightarrow {x^3} = 20 + 14\sqrt 2 - \left( {14\sqrt 2 - 20} \right) - 3\sqrt[3]{{{{14}^2}.2 - 400}}.x\\ \Leftrightarrow {x^3} = 40 - 3\sqrt[3]{{ - 8}}x\\ \Leftrightarrow {x^3} - 6x - 40 = 0\\ \Leftrightarrow {x^3} - 4{x^2} + 4{x^2} - 16x + 10x - 40 = 0\\ \Leftrightarrow {x^2}\left( {x - 4} \right) + 4x\left( {x - 4} \right) + 10\left( {x - 4} \right) = 0\\ \Leftrightarrow \left( {x - 4} \right)\left( {\underbrace {{x^2} + 4x + 10}_{ > 0}} \right) = 0\\ \Leftrightarrow x = 4 \end{array}$
