N4-12n2+16 как это решить

N⁴ - 12n² + 16 = 0

Заменим n² = x:

x² - 12x + 16 = 0 D = b²-4ac = 144 - 64 = 80 = (4√5) ²

x₁ = (-b + √D) / 2a = (12 + 4√5) / 2 = 6 + 2√5

x₂ = (-b - √D) / 2a = (12 - 4√5) / 2 = 6 - 2√5

n² = 6 + 2√5 n² = 6 - 2√5

n = √ (6+2√5) n = √ (6-2√5)

n = - √ (6+2√5) n = - √ (6-2√5)

проверим: (√ (6+2√5)) ⁴ - 12 (√ (6+2√5)) ² + 16 = (6+2√5) ² - 12 (6+2√5) + 16 =

= 36 + 24√5 + 20 - 72 - 24√5 + 16 = 72 - 72 = 0

(√ (6-2√5)) ⁴ - 12 (√ (6-2√5)) ² + 16 = (6-2√5) ² - 12 (6-2√5) + 16 =

= 36 - 24√5 + 20 - 72 + 24√5 + 16 = 72 - 72 = 0

Ответ: {√ (6+2√5); √ (6-2√5); - √ (6+2√5); - √ (6-2√5) }

Y=n²

y²-12e+16=0

y=6+-√ (36-16) = 6+-2√5

n=+-√ (6+-2√5))