Question

1) -5x4 + 30x2 - 25 =0
2) 4x4 + 8x2 - 32 =0
3) x4 - 3x2 + 2 =0
Решите

Answer 1

$- 5 {x}^{4} + 30 {x}^{2} - 25 = 0 \\ {x}^{2} = t \geqslant 0 \\ - 5t {}^{2} + 30t - 2 5 = 0 \\ 5 {t}^{2} - 30t + 25 = 0 \\ {t}^{2} - 6t + 5 = 0 \\ t1 = 1 \\ t2 = 5 \\ x {}^{2} = 1 \\ {x}^{2} = 5 \\ x = 1 \\ x = - 1 \\ x = \sqrt{5} \\ x = - \sqrt{5}$

$4 {x}^{4} + 8 {x}^{2} - 32 = 0 \\ {x}^{2} = t \geqslant 0 \\ t {}^{2} + 2t - 8 = 0 \\ t1 = - 4 \\ t2 = 2 \\ x {}^{2} = 2 \\ x = \sqrt{2} \\ x = - \sqrt{2}$

$x {}^{4} - 3 {x}^{2} + 2 = 0 \\ {x}^{2} = t \geqslant 0 \\ {t}^{2} - 3t + 2 = 0 \\ t1 = 2 \\ t2 = 1 \\ x { }^{2} = 1 \\ x {}^{2} = 2 \\ x = 1 \\ x = - 1 \\ x = \sqrt{2} \\ x = - \sqrt{2}$