Решите систему уравнений [latex] \left \{ {{x²+y²=58} \atop {xy=21}} \right. [/latex]

[latex] \left \{ {{ x^{2} + y^{2} =58} \atop {y= \frac{21}{x} }} \right. }[/latex] [latex] x^{2} + (\frac{21}{x}) ^{2} =58[/latex] [latex] x^{2} + \frac{441}{ x^{2} } =58[/latex] [latex] x^{4} - 58 x^{2} + 441 = 0[/latex] [latex]t = x^{2} [/latex] [latex] t^{2} - 58 t + 441 = 0[/latex] [latex]D = 3364 - 4*441=1600[/latex] [latex] t_{1} = \frac{58+40}{2}=49[/latex] [latex] t_{2} = \frac{58-40}{2}=9[/latex] [latex]x_{1}=\sqrt{49} = 7[/latex] [latex]x_{2}=\sqrt{49} = -7[/latex] [latex]x_{3}=\sqrt{9} = 3[/latex] [latex]x_{4}=\sqrt{9} = -3[/latex] [latex]y_{1}=\frac{21}{7}= 3[/latex] [latex]y_{2}=\frac{21}{-7}= -3[/latex] [latex]y_{3}=\frac{21}{3}= 7[/latex] [latex]y_{4}=\frac{21}{-3}= -7[/latex]