Question

equações biquadradas 4 x elevado a 4 menos 5 x elevado a 2 + 1 = 0

Answer 1

Ola 

4x⁴ - 5x² + 1 = 0

y = x²

4y² - 5y + 1 = 0

delta
d² = 25 - 16 = 9
d = 3

y1 = (5 + 3)/8 = 8/8 = 1
y2 = (5 - 3)/8 = 2/8 = 1/4 

x1 = √1 = 1
x2 = -√1 = -1

x3 = √(1/4) = 1/2
x4 = -√(1/4) = -1/2 

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Answer 2

Vamos lá :

4x⁴ - 5x² + 1 = 0      ÷  4

x⁴ - 5x²/4 + 1/4 = 0

(x²)² - 5x²/4 + 1/4 = 0

x² = h

h² - 5h/4 + 1/4 = 0           ×  4
4h² - 5h + 1 = 0

a = 4 ; b = - 5 ; c = 1

Δ = b² - 4ac
Δ = (-5)² - 4.4.1
Δ = 25 - 16
Δ = 9          ⇒ √Δ = 3

Aplica a formula de Bhaskara :

x = - b +/- √Δ / 2a
x = - (- 5) +/- 3 / 2.4
x = 5 +/-  3 / 8

x' = 5 + 3/8 = 8/8 = 1
x'' = 5 - 3/8 = 2/8 ÷ 2 = 1 / 4

x² = h'      x²  = h''
x² = 1       x² = 1/4
x = +/- √1 x = +/- √1/4
x = +/- 1   x = +/- 1/2

S = {- 1/2 ,- 1,1/ 2 , 1}

Espero ter ajudado !!!