Răspuns:
Explicație pas cu pas:
x⁴-10x²+9 = 0
x² = t => t²-10t+9 = 0
a = 1 ; b = -10 ; c = 9 ; Δ = b²-4ac = 100-36 = 64 ; √Δ=√64 = 8
t₁,₂ = (-b±√Δ)/2a = (10±8)/2 => t₁ = 1 ; t₂ = 9
x² = 1 => x₁,₂ = ±1 ;
x² = 9 => x₃,₄ = ±3
x⁴-12x²-64=0
x² = t => t²-12t-64 = 0 ;
a = 1 ; b = -12 ; c = -64 ; Δ = 144+256 = 400 => √Δ = 20
t₁,₂ = (12±20)/2 = > t₁ = -4 ; t₂ = 16
x² = -4 => x₁,₂ = ±2i ∈ C
x² = 16 => x₃,₄ = ±4
x⁴+17x²+72=0
x² = t => t²+17t+72 = 0 ; a = 1 ; b = 17 ; c = 72 ; Δ = 289-288 = 1
t₁,₂ = (-17±1)/2 => t₁ = -9 ; t₂ = -8
x² = -9 => x₁,₂ = ±3i ∈ C
x² = -8 => x₃,₄ = ±2i√2 ∈ C
16x⁴+40x²+9=0
x² = t => 16t² +40t +9 = 0
a = 16 ; b = 40 ; c = 9 ; Δ = 1600-576 = 1024 ; √Δ = √1024 = 32
t₁,₂ = (-40±32)/32 = > t₁ = -72/32 = -9/4 ; t₂ = -8/32 = -1/4
x² = -9/4 => x₁,₂ = ±3i/2 ∈ C
x² = -1/4 => x₃,₄ = ±i/2 ∈ C
i = √-1 ; i² = -1
