16х⁴ - 64х² + 64 + 11(4х² - 8) + 28 =0
16х⁴ - 64х² + 64 + 44х² - 88 + 28 =0
16х⁴- 20х² + 4 = 0 | :4
4х⁴ - 5х² + 1 = 0
Замена: х² = у
4у² - 5у + 1 = 0
D = 25 - 4*4*1 = 25 - 16 = 9 D >0, продолжим решение
у₁ = (5+√9)/(2*4) = (5+3)/8 = 1
х₁ = 1
х₂ = -1
у₂ = (5 -√9)/(2*4) = (5-3)/8 = 2/8 = 1/4
х₃ = + √(1/4) = 1/2
х₄ = -√(1/4) = - 1/2
ответ: 1; -1; 1/2; -1/2
16х⁴ - 64х² + 64 + 11(4х² - 8) + 28 =0
16х⁴ - 64х² + 64 + 44х² - 88 + 28 =0
16х⁴- 20х² + 4 = 0 | :4
4х⁴ - 5х² + 1 = 0
Замена: х² = у
4у² - 5у + 1 = 0
D = 25 - 4*4*1 = 25 - 16 = 9 D >0, продолжим решение
у₁ = (5+√9)/(2*4) = (5+3)/8 = 1
х₁ = 1
х₂ = -1
у₂ = (5 -√9)/(2*4) = (5-3)/8 = 2/8 = 1/4
х₃ = + √(1/4) = 1/2
х₄ = -√(1/4) = - 1/2
ответ: 1; -1; 1/2; -1/2