Question

50 балів ......................

Answer 1

$\sqrt{x + y} + \sqrt{x - y} = 10 \\ \sqrt{ {x}^{2} - {y}^{2} } = 9 \\ \\ \sqrt{x + y} + \sqrt{x - y} = 10 \\ \sqrt{ (x - y)(x + y) } = 9 \\ \\ a = \sqrt{x + y} \geqslant 0 \\ b = \sqrt{x - y} \geqslant 0 \\ \\ a + b = 10 \\ ab = 9 \\ \\ b = 10 - a \\ a(10 - a) = 9 \\ {a}^{2} - 10a + 9 = 0 \\ (a - 9)(a - 1) = 0 \\ a_1= 9 = >b_1 =10 - a_1 = 1\\ a_2 = 1 = > b_2 =10 - a_2 = 9$
$\sqrt{x + y} = 9 \\ \sqrt{x - y} = 1 \\ x + y = 81 \\ x - y = 1 \\ 2x = 82 = > x_1 = 41 = > y_1 = 40\\ \\ \sqrt{x + y} = 1 \\ \sqrt{x - y} = 9 \\ x + y = 1 \\ x - y =81 \\ 2x = 82 = > x_2 = 41 = > y_2 = - 40$
Ответ
$\\ x_1 = 41 \\ y_1 = 40 \\ \\ x_2 = 41 \\ y_2 = - 40$