Решебник по алгебре 7 класс Мерзляк ФГОС Задание 737

 

\[\boxed{\text{737\ (737).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[x + y = 6;\ \ \ \ \ \text{xy} = - 3\]

\[1)\ x³y² + x²y³ =\]

\[= x^{2}y^{2}(x + y) = ( - 3)^{2} \cdot 6 =\]

\[= 9 \cdot 6 = 54\]

\[2)\ (x - y)^{2} = x² - 2xy + y^{2} =\]

\[= x^{2} + 2yx + y^{2} - 4xy =\]

\[= (x + y)^{2} - 4xy =\]

\[= 6^{2} - 4 \cdot ( - 3) = 36 + 12 = 48\]

\[3)\ x^{4} + y^{4} =\]

\[= x^{4} + y^{4} + 2x^{2}y^{2} - 2x^{2}y^{2} =\]

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

\[= \left( x^{2} + y^{2} \right)^{2} - 2 \cdot 9 =\]

\[= \left( x^{2} + y^{2} \right)^{2} - 18 =\]

\[= \left( x^{2} + y^{2} + 2xy - 2xy \right)^{2} - 18 =\]

\[= \left( x^{2} + y^{2} + 2xy - 2 \cdot ( - 3) \right)^{2} - 18 =\]

\[= \left( (x + y)^{2} + 6 \right)^{2} - 18 =\]

\[= \left( 6^{2} + 6 \right)^{2} - 18 =\]

\[= (36 + 6)^{2} - 18 = 42^{2} - 18 =\]

\[= 1764 - 18 = 1746\]

\[\boxed{\text{737.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[(2a - 3x)^{2} + (x - 1)^{2} =\]

\[= 10 \cdot (x - 2)(x + 2)\]

\[4a^{2} - 12ax + 9x^{2} + x^{2} - 2x + 1 =\]

\[= 10 \cdot \left( x^{2} - 4 \right)\]

\[- 2x - 12ax = - 4a^{2} - 41\]

\[- 2x \cdot (1 + 6a) = - 4a^{2} - 41\]

\[1 + 6a = 0\]

\[6a = - 1\ \ \]

\[a = - \frac{1}{6}\]

\[при\ \ a = - \frac{1}{6}\ уравнение\ \]

\[не\ имеет\ корней:\]

\[4 \cdot \left( - \frac{1}{6} \right) - 12x \cdot \left( - \frac{1}{6} \right) - 2x =\]

\[= - 41\]

\[- \frac{2}{3} + 2x - 2x = - 41\]

\[0x = - 41 + \frac{2}{3}\]

\[0 \neq - 40\frac{1}{3}\]

\[Ответ:\ при\ a = - \frac{1}{6}.\]