9х⁴ - 85х² + 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 .