Решебник по алгебре 7 класс Мерзляк ФГОС Задание 876

 

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\[f(x) = 4x - 3\ \ \ и\ \ \ \]

\[g(x) = 3x - 2\]

\[4x - 3 = 3x - 2\ \ \]

\[x = 1\ \ \]

\[f(1) = 1\]

\[1)\ f(x) > g(x)\ при\ x > 1;\ \ \]

\[2)\ f(x) < g(x)\ при\ \ x < 1.\]

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

\[1)\ x³y² + x²y³ =\]

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

\[= 9 \cdot 6 = 54\]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[= 1764 - 18 = 1746\]