Question

решить систему уравнений { 3x-2y=1 ; xy=1

Answer 1

$\left \{ {{3x-2y=1} \atop {xy=1}} \right. </p> <p>\left \{ {{y=\frac{1}{x} } \atop {3x-2y=1}} \right.$

$3x-2*\frac{1}{x}=1</p> <p>3x^{2}-2=x</p> <p>3x^{2}-x-2=0$$D=b2-4ac=(-1)^{2}-4*3*(-2)=1+24=25=5^{2}, D>0</p> <p>x_{1}=\frac{-b-\sqrt{D} }{2a}=\frac{1-5}{2*3}=\frac{-4}{6}=-\frac{2}{3}</p> <p>x_{2}=\frac{-b+\sqrt{D} }{2a}=\frac{1+5}{2*3}=\frac{6}{6}=1$