Question

Сумма двух чисел равна 1,4 а сумма их квадратов равна 1. Найдите эти числа.

Answer 1

$x + y = 1.4 \ {x}^{2} + {y}^{2} = 1 \ \ {(x + y)}^{2} = 1.96 \ {x}^{2} + {y}^{2} = 1 \ \ {x}^{2} + 2xy + {y}^{2} = 1.96 \ {x}^{2} + {y}^{2} = 1 \ \ 1 + 2xy = 1.96 \ x + y = 1.4 \ \ 2xy = 0.96 \ x + y = 1.4 \ \ xy = 0.48 \ x + y = 1.4 \ \ y = 1.4 - x \ x(1.4 - x) = 0.48 \ \ \ y = 1.4 - x \ 1.4x - {x}^{2} = 0.48 \ \ y = 1.4 - x \ {x}^{2} - 1.4x + 0.48 = 0 \ \ d = {b}^{2} - 4ac = 1.96 - 4 times 0.48 = 0.04 \ x1 = frac{1.4 + 0.2}{2} = frac{1.6}{2} = 0.8 \ x2 = frac{1.4 - 0.2}{2} = frac{1.2}{2} = 0.6 \ \ y1 = 1.4 - 0.8 = 0.6 \ y2 = 1.4 - 0.6 = 0.8$
Ответ: (0,8; 0,6), (0,6; 0,8)