Question

(x2-3)×(x2+4)+12=7×(x2+2)+2

Answer 1

(x² - 3) .(x² + 4) + 12 = 7.(x² + 2) + 2
x⁴ + 4x² - 3x² - 12 + 12 = 7x² + 14 + 2
x⁴ + x² = 7x² + 16
x⁴ + x² - 7x² - 16 = 0
x⁴ - 6x² - 16 = 0
(x²)² - 6x² - 16 = 0
y² - 6y - 16 = 0
a = 1; b = - 6; c = - 16

Δ = b² - 4ac
Δ = (-6)² - 4.1.(-16)
Δ = 36 + 64
Δ = 100

y = - b +/- √Δ      =  - (-6) +/- √100 
      ---------------       ---------------------
               2a                     2.1

y = 6 + 10
      ------------   = 16/2   = 8
           2

y = 6 - 10      = - 4/2 = - 2
      -----------
           2

y = - 2
x² = y
x² = - 2   (descartar)

y = 8
x² = 8
x = √8
x = √4.√2
x = +/- 2√2

R.: x = 2√2 e x = - 2√2