proszę o pomoc w zadaniach a) x⁴-1=0 b) 3x⁴=-6x²+9 c) x⁴+10x²-11=0
a)
x^4-1=0
(x^2-1)(x^2+1)=0
(x-1)(x+1)(x^2+1)=0
x-1=0 v x+1=0
x=1, x=-1
b) 3x^4=-6x^2+9
3x^4+6x^2-9=0
x^2=t
3t^2+6t-9=0
\Delta=36+108=144
t_1=\frac{-6-12}{6}=-3 odrzucamy
t_2=\frac{-6+12}{6}=1
x^2=1
c)
x^4+10x^2-11=0
t>0
t^2+10t-11=0
\Delta=100+44=144
t_1=\frac{-10-12}{2}=-11 odrzucamy (t>0)
t_2=\frac{-10+12}{2}=1