Question

Решить уравнение
${x}^{4} - 10 {x}^{2} + 9 = 0$

Answer 1

$x^4 - 10x^2 + 9 = 0$

$x^2=t,t \ge 0$

$t^2-10t+9=0$

$\Delta=(-10)^2-4 \cdot 1 \cdot 9=100-36=64$

$\sqrt{\Delta} = \sqrt{64}=8$

$t_1= \frac{10-8}{2}= \frac{2}{2}=1$

$t_2= \frac{10+8}{2}= \frac{18}{2}=9$

$x_1= \sqrt{1}= 1$

$x_2=- \sqrt{1}=-1$

$x_3= \sqrt{9}=3$

$x_4= -\sqrt{9}=-3$