\left \{ {{y=\frac{1}{x} } \atop {3x-2y=1}} \right." alt="\left \{ {{3x-2y=1} \atop {xy=1}} \right.
\left \{ {{y=\frac{1}{x} } \atop {3x-2y=1}} \right." align="absmiddle" class="latex-formula">
3x^{2}-2=x
3x^{2}-x-2=0" alt="3x-2*\frac{1}{x}=1
3x^{2}-2=x
3x^{2}-x-2=0" align="absmiddle" class="latex-formula">
0
x_{1}=\frac{-b-\sqrt{D} }{2a}=\frac{1-5}{2*3}=\frac{-4}{6}=-\frac{2}{3}
x_{2}=\frac{-b+\sqrt{D} }{2a}=\frac{1+5}{2*3}=\frac{6}{6}=1" alt="D=b2-4ac=(-1)^{2}-4*3*(-2)=1+24=25=5^{2}, D>0
x_{1}=\frac{-b-\sqrt{D} }{2a}=\frac{1-5}{2*3}=\frac{-4}{6}=-\frac{2}{3}
x_{2}=\frac{-b+\sqrt{D} }{2a}=\frac{1+5}{2*3}=\frac{6}{6}=1" align="absmiddle" class="latex-formula">