Question

Найти значение 16х⁴-64х²+64+11(4х²-8)+28=0

Answer 1

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