Question

Rezolvati in multimea numerelor reale ecuatia | x^2 -2 | - |x - radical din 2 |= 0

Answer 1

$/x^{2} -2= \frac{+}{-}(x- \sqrt{2})$. cosider cele doua ecuatii:
[tex] x^{2} -2=x- \sqrt{2},adica. x^{2} -x+( \sqrt{2}-2)=0;avem;a=1;b=-1; [/tex]
c=$\sqrt{2}-2$,deci Δ=$b^{2}-4*a*c=1-4*( \sqrt{2}-2)= 1+8-4 \sqrt{2}=(1-2 \sqrt{2})^2$ se obtine X1=(1+1-2√2)/2=1-√2; 
X2=(1-1+2√2)/2=√2.
Apoi a doua ec: $x^{2} +x+( \sqrt{2}+2)=0,$, avem 
Δ=$\frac{1+4( \sqrt{2}+2) }{2}=(1+2 \sqrt{2})^{2}$, X3=-1-√2 si X4=X2=√2.