[tex] {x}^{4} - 12 {x}^{2} - 11 = 0 \\ {x}^{2} = a \: , \: \: a \geqslant 0 \\ {a}^{2} - 12a - 11 = 0 \\ D = ( - 12) {}^{2} - 4 \times ( - 11) = \\ = 144 + 44 = 188 \: \: ( \sqrt{D} = 2 \sqrt{47} ) \\ a_{1} = \frac{12 - 2 \sqrt{47} }{2} = \frac{2(6 - \sqrt{47}) }{2} = 6 - \sqrt{47} \\ a_{2} = \frac{12 + 2 \sqrt{47} }{2} = \frac{2(6 + \sqrt{47}) }{2} = 6 + \sqrt{47} [/tex]

Первый корень не подходит

[tex]x {}^{2} = 6 + \sqrt{47} \\ x_{1} = - \sqrt{6 + \sqrt{47} } \\ x_{2} = \sqrt{6 + \sqrt{47} } [/tex]