Для первой пропорции:
(a^2 - b^2) / x = (a^2 - 2ab + b^2) / (x^2 - y^2) / xy = (x - 2y + y) / (x - y) / x = 1 / (x - y) / x = 1 / x - y = x / x = x / b + 1 = 1 / b + 1 = (b + 1) / b
x = b + 1
Для второй пропорции:
(14a + 7b) / (3b^2 - 12a^2) = x / (2a - b(7(2a + b)) / (3(2b - 2a)(b - a)) = x / (2a - b(7(2a + b)) / (3(-2)(2a - b)(a - b)) = x / (-2)(a - b-7(2a + b) / 6(2a - b)(b - a) = x / (a - b(7b + 2a) / (3b - 3a) = x / (a - b(7b + 2a) / 3(b - a) = x / -(b - a-(7b + 2a) / 3(b - a) = x / (a - b(3(-2) - 7(2)) / 3(1 - 2) = x / (2 - 1(-6 - 14) / 3(-1) = x / -20 / -3 = x = 20 / 3
Для первой пропорции:
(a^2 - b^2) / x = (a^2 - 2ab + b^2) /
(x^2 - y^2) / xy = (x - 2y + y) /
(x - y) / x = 1 /
(x - y) / x = 1 /
x - y = x /
x = x / b +
1 = 1 / b +
1 = (b + 1) / b
x = b + 1
Для второй пропорции:
(14a + 7b) / (3b^2 - 12a^2) = x / (2a - b
(7(2a + b)) / (3(2b - 2a)(b - a)) = x / (2a - b
(7(2a + b)) / (3(-2)(2a - b)(a - b)) = x / (-2)(a - b
-7(2a + b) / 6(2a - b)(b - a) = x / (a - b
(7b + 2a) / (3b - 3a) = x / (a - b
(7b + 2a) / 3(b - a) = x / -(b - a
-(7b + 2a) / 3(b - a) = x / (a - b
(3(-2) - 7(2)) / 3(1 - 2) = x / (2 - 1
(-6 - 14) / 3(-1) = x /
-20 / -3 =
x = 20 / 3