3. Решить уравнение: a) 36x² - 5 - (6x - 5)² = 0 б) (x+5)² - (x - 1)² = 48 в) (2x - 3)² + (3-4x)(x + 5) = 82

a) $$36x^2 - 5 - (6x-5)^2 = 0$$ $$36x^2 - 5 - (36x^2 - 60x + 25) = 0$$ $$36x^2 - 5 - 36x^2 + 60x - 25 = 0$$ $$60x - 30 = 0$$ $$60x = 30$$ $$x = \frac{30}{60} = \frac{1}{2}$$ Ответ: $$x = \frac{1}{2}$$ б) $$(x+5)^2 - (x-1)^2 = 48$$ $$(x^2 + 10x + 25) - (x^2 - 2x + 1) = 48$$ $$x^2 + 10x + 25 - x^2 + 2x - 1 = 48$$ $$12x + 24 = 48$$ $$12x = 24$$ $$x = \frac{24}{12} = 2$$ Ответ: $$x = 2$$ в) $$(2x-3)^2 + (3-4x)(x+5) = 82$$ $$(4x^2 - 12x + 9) + (3x + 15 - 4x^2 - 20x) = 82$$ $$4x^2 - 12x + 9 + 3x + 15 - 4x^2 - 20x = 82$$ $$-29x + 24 = 82$$ $$-29x = 58$$ $$x = \frac{58}{-29} = -2$$ Ответ: $$x = -2$$