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