994. Решите уравнение: a) (x - 7)2+3=(x-2)(x+2); б) (x+6)²-(x-5)(x + 5) = 79; в) (2x - 3)² - (7-2x)² = 2;

Решим уравнение:

1. a) $$(x - 7)^2+3=(x-2)(x+2)$$ $$x^2 - 14x + 49 + 3 = x^2 - 4$$ $$x^2 - 14x + 52 - x^2 + 4 = 0$$ $$-14x + 56 = 0$$ $$-14x = -56$$ $$x = 4$$
2. б) $$(x+6)^2 - (x-5)(x+5) = 79$$ $$x^2 + 12x + 36 - (x^2 - 25) = 79$$ $$x^2 + 12x + 36 - x^2 + 25 - 79 = 0$$ $$12x - 18 = 0$$ $$12x = 18$$ $$x = \frac{18}{12} = \frac{3}{2} = 1.5$$
3. в) $$(2x - 3)^2 - (7-2x)^2 = 2$$ $$(2x-3)^2 - (2x-7)^2 = 2$$ $$4x^2 - 12x + 9 - (4x^2 - 28x + 49) = 2$$ $$4x^2 - 12x + 9 - 4x^2 + 28x - 49 - 2 = 0$$ $$16x - 42 = 0$$ $$16x = 42$$ $$x = \frac{42}{16} = \frac{21}{8} = 2.625$$

Ответ: a) x=4; б) x=1.5; в) x=2.625