Решите уравнение 9x^4-10x^2+1=0.

Ответ:

\[9x^{4} - 10x^{2} + 1 = 0\]

\[Пусть\ x^{2} = t \geq 0:\]

\[9t^{2} - 10t + 1 = 0\]

\[D_{1} = 25 - 9 = 16\]

\[t_{1} = \frac{5 + 4}{9} = 1;\ \ \ t_{2} = \frac{5 - 4}{9} = \frac{1}{9}.\]

\[1)\ x^{2} = 1\]

\[x = \pm 1.\]

\[2)\ x^{2} = \frac{1}{9}\]

\[x = \pm \frac{1}{3}.\]

\[Ответ:x = \pm 1;\ \ x = \pm \frac{1}{3}.\]