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EGGzy
a fost răspuns

Numarul solutiilor reale ale ecuatiei x^4+2x^3+2x+1=0?

Răspuns :

Albatran
E o ecuatie reciproca (termenii egali departatide extemi au coeficienti egali)


impartim cu x²
x²+2x+2/x+1/x²=0

x²+1/x² +2(x+1/x)=0
fie x+1/x=t
aunci
t²-2+2t=0

t²+2t-2=0

t1,2=(-2+-√12)/2=(-2+-2√3)/2=-1+-√3

x+1/x=-1-√3
x²+(1+√3)x+1=0

Δ=4+2√3-4=2√3>0 ..2 rad reale distincte

x+1/x= -1+√3
x²+(1-√3)x+1=0
Δ=4-2√3-4=-2√3<0 nici o  radacina reala

 total 2+0=2 radacini reale

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