ГДЗ по алгебре 8 класс Макарычев Задание 695

\[\boxed{\text{695\ (695).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\left( x\sqrt{3} + \sqrt{2} \right)^{2} + \left( x\sqrt{3} - \sqrt{2} \right)^{2} =\]

\[= 10x\]

\[3x^{2} + 2x\sqrt{6} + 2 + 3x^{2} - 2x\sqrt{6} + 2 =\]

\[= 10x\]

\[6x^{2} - 10x + 4 = 0\ \ \ \ \ \ \ |\ :2\]

\[3x^{2} - 5x + 2 = 0\]

\[D = 25 - 24 = 1\]

\[x_{1,2} = \frac{5 \pm 1}{6} = 1;\frac{2}{3}\]

\[Ответ:x = \frac{2}{3};\ \ x = 1.\]

\[\left( 1 - y\sqrt{5} \right)^{2} + \left( 1 + y\sqrt{5} \right)^{2} = 9y\]

\[1 - 2y\sqrt{5} + 5y^{2} + 1 + 2y\sqrt{5} + 5y^{2} =\]

\[= 9y\]

\[10y^{2} - 9y + 2 = 0\]

\[D = 81 - 80 = 1\]

\[y_{1,2} = \frac{9 \pm 1}{20} = \frac{1}{2};\frac{2}{5}\]

\[Ответ:y = 0,4;\ \ y = 0,5\text{.\ }\]