Решите уравнение:

9*x^4-85*x^2+36=0

9 х⁴ - 85 х² + 36 = 0

замена: х² = n

9n² - 85n + 36 = 0

D = (-85) ² - 4*9*36 = 7225 - 1296 = 5929 = 77²

D>0

n₁ = (- (- 85) - 77) / (2*9) = (85 - 77) / 18 = 8/18 = 4/9

n₂ = (- (- 85) + 77) / (2*9) = (85 + 77) / 18 = 162/18 = 9

x² = 4/9

x² - 4/9 = 0

x² - (2/3) ² = 0

(x - 2/3) (x + 2/3) = 0

x - 2/3 = 0

x₁ = 2/3

x + 2/3 = 0

x₂ = - 2/3

x² = 9

x - 9 = 0

x² - 3² = 0

(x - 3) (x + 3) = 0

x - 3 = 0

x₁ = 3

x + 3 = 0

x₂ = - 3

Ответ: х₁ = - 3; х₂ = - 2/3; х₃ = 2/3; х₄ = 3.