20.4^(x²+2) - 9 * 2^(x²+2) + 8 = 0

20.4^(x²+2) - 9 * 2^(x²+2) + 8 = 0

(2²)^(x²+2) - 9 * 2^(x²+2) + 8 = 0

(2^(x²+2))² - 9 * 2^(x²+2) + 8 = 0

Замена: y = 2^(x²+2)

y² - 9y + 8 = 0

D = b² - 4ac = (-9)² - 4*1*8 = 81 - 32 = 49

y₁ = (-b + √D) / (2a) = (9 + √49) / (2*1) = (9 + 7) / 2 = 16/2 = 8

y₂ = (-b - √D) / (2a) = (9 - √49) / (2*1) = (9 - 7) / 2 = 2/2 = 1

1) 2^(x²+2) = 8

2^(x²+2) = 2³

x² + 2 = 3

x² = 1

x₁ = 1; x₂ = -1

2) 2^(x²+2) = 1

2^(x²+2) = 2⁰

x² + 2 = 0

x² = -2 (нет решений, так как x² ≥ 0)

Ответ: x₁ = 1; x₂ = -1