ГДЗ по алгебре 11 класс Никольский Параграф 7. Равносильность уравнений и неравенств Задание 7

\[\boxed{\mathbf{7.}}\]

\[\textbf{а)}\ (2x - 3)^{7} = (x + 1)^{7}\]

\[2x - 3 = x + 1\]

\[x = 4.\]

\[\textbf{б)}\ (3x + 1)^{5} = (x + 9)^{5}\]

\[3x + 1 = x + 9\]

\[2x = 8\]

\[x = 4.\]

\[\textbf{в)}\ \left( 3x^{2} - 4x \right)^{9} = \left( x^{2} - 8x \right)^{9}\]

\[3x^{2} - 4x = x^{2} - 8x\]

\[2x^{2} + 4x = 0\]

\[2x(x + 2) = 0\]

\[x = 0;\ \ x = - 2.\]

\[\textbf{г)}\ \left( 5x^{2} + 4x \right)^{3} = \left( x^{2} + 2x \right)^{3}\]

\[5x^{2} + 4x = x^{2} + 2x\]

\[4x^{2} + 2x = 0\]

\[4x(x + 0,5) = 0\]

\[x = 0;\ \ x = - 0,5.\]