Question

Equação biquadrada, me ajudem!
(2x²-5)² =10(2x²-5)+39

Answer 1

• (2x² -5) = a

a² = 10a +39

a² -10a -39 = 0

$39|3\\13|13$

-b = 13 -3 = 10

{13 , -3}

• (2x² -5) = a

2x² -5 = 13

2x² = 13 + 5

x² = 18/2

x = ±√9

x = ± 3

2x² -5 = -3

2x² = -3 +5

x² = 2/2

x = ±√1

x = ± 1

{3 , -3 , 1 , -1}

Answer 2

2x² - 5 = y ∴ x = √[(y + 5)/2]

y² - 10y - 39 = 0

y = {10 ⁺₋ √[100 - 4*(-39)]}/2

y = {10 ⁺₋ √[100 + 156]}/2

y = {10 ⁺₋ √[256]}/2

y = {10 ⁺₋ 16}/2

y' = -6/2 ∴ y' = -3

y" = 26/2 ∴ y" = 13

x' = √[(-3 + 5)/2]  = √1  ∴ x' = 1

x" = √[(13 + 5)/2] = √9 ∴ x" = 3