(–1/7)x² + (6/7)x – 1 = 0

x² – 6x + 7 = 0

D = (–6)² – 4·7 = 8 = (2√2)²

x₁ = (6 – 2√2) / 2 = 3 – √2

x₂ = (6 + 2√2) / 2 = 3 + √2

x⁴ – 7x² + 6 = 0

Введем замену t = x², t ≥ 0, тогда x = ±√t

t² – 7t + 6 = 0

D = (–7)² – 4·6 = 25 = 5²

t₁ = (7 – 5) / 2 = 1 ⇒ x = ±√1 ⇒ x₁ = –1, x₂ = 1

t₂ = (7 + 5) / 2 = 6 ⇒ x = ±√6 ⇒ x₁ = –√6, x₂ = √6