748. При каких значениях х верно равенство: a) $$(5x + 3)^2 = 5(x + 3)$$; б) $$(3x + 10)^2 = 3(x + 10)$$; в) $$(3x - 8)^2 = 3x^2 - 8x$$; г) $$(4x + 5)^2 = 5x^2 + 4x$$;

a) $$(5x + 3)^2 = 5(x + 3)$$ $$(5x + 3)^2 - 5(x + 3) = 0$$ $$(5x + 3)(5x + 3 - 5) = 0$$ $$(5x + 3)(5x - 2) = 0$$ $$5x + 3 = 0$$ или $$5x - 2 = 0$$ $$x_1 = -\frac{3}{5}$$ или $$x_2 = \frac{2}{5}$$ б) $$(3x + 10)^2 = 3(x + 10)$$ $$(3x + 10)^2 - 3(x + 10) = 0$$ $$(3x + 10)(3x + 10 - 3) = 0$$ $$(3x + 10)(3x + 7) = 0$$ $$3x + 10 = 0$$ или $$3x + 7 = 0$$ $$x_1 = -\frac{10}{3}$$ или $$x_2 = -\frac{7}{3}$$ в) $$(3x - 8)^2 = 3x^2 - 8x$$ $$9x^2 - 48x + 64 = 3x^2 - 8x$$ $$6x^2 - 40x + 64 = 0$$ $$3x^2 - 20x + 32 = 0$$ $$D = (-20)^2 - 4 * 3 * 32 = 400 - 384 = 16$$ $$x_1 = \frac{20 + 4}{6} = \frac{24}{6} = 4$$ $$x_2 = \frac{20 - 4}{6} = \frac{16}{6} = \frac{8}{3}$$ г) $$(4x + 5)^2 = 5x^2 + 4x$$ $$16x^2 + 40x + 25 = 5x^2 + 4x$$ $$11x^2 + 36x + 25 = 0$$ $$D = 36^2 - 4 * 11 * 25 = 1296 - 1100 = 196$$ $$x_1 = \frac{-36 + 14}{22} = \frac{-22}{22} = -1$$ $$x_2 = \frac{-36 - 14}{22} = \frac{-50}{22} = -\frac{25}{11}$$