Question

$9x^{4}-9x^{2}+2=0$ помогите пожалуйста

Answer 1

9x⁴ - 9x² + 2 = 0

Сделаем замену x² = m , m ≥ 0

9m² - 9m + 2 = 0

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

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