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9x⁴ - 9x² + 2 = 0

Сделаем замену x² = m , m ≥ 0

9m² - 9m + 2 = 0

D = (- 9)² - 4 * 9 * 2 = 81 - 72 = 9 = 3²

$m_{1} = \frac{9+3}{18}= \frac{12}{18}= \frac{2}{3}\\\\m_{2}= \frac{9-3}{18}= \frac{6}{18}= \frac{1}{3} \\\\x^{2} =\frac{2}{3} \\\\x_{1}= \sqrt{\frac{2}{3}}= \frac{\sqrt{6}} {3}\\\\x_{2}=- \sqrt{\frac{2}{3}}=- \frac{\sqrt{6}} {3} \\\\x^{2} =\frac{1}{3}\\\\x_{3} =\sqrt{\frac{1}{3}}= \frac{\sqrt{3}} {3}\\\\ x_{4}=- \sqrt{\frac{1}{3}}=- \frac{\sqrt{3}} {3}$