Question

x^4-10x^2+9 am nevoie de toate radacinile reale

Answer 1

Răspuns

x^2=y    y>,0

y^2-10y+9=0

Determinantul D=10^2-4*9=100-36=64

y1=(10-√64)/2=(10-8)/2=1

y2=(10+8)/2=18/2=9

x²=1=>   x1=-1    x2=1

x²=9=> x3/4=√9=+/-3

Explxicație pas cu pas:

Answer 2

x⁴-10x²+9=0

Notam x²=t

t²-10t+9=0

Δ=100-36=64

t₁=(10-√64)/2=(10-8)/2=1

t₂=(10+√64)/2=(10+8)/2=9

Pt.t₁=1=>x²=t₁=>x²=1=>x=±√1=>x₁=1;x₂=-1

Pt.t₂=9=>x²=t₂=>x²=9=>x=±√9=>x₃=3;x₄=-3

x∈{±1;±3}