Question

Помогите пожалуйста решить систему уравнений
x+y=13
√ x+√ y=5

Answer 1

x+y=13
√ x+√ y=5

x+y=13
(√ x+√ y)^2 = 25

x + y = 13
x + y + 2√(xy) = 25

x + y = 13
2√(xy) = 25 - 13

x + y = `3
2√(xy) = 12

x + y = 13
√(xy) = 6

x + y = 13
xy = 36

y = 13 - x
x*(13 - x) = 36
x^2 - 13x + 36 = 0
D = 169 - 4*1*36 = 169 - 144 = 25
x1 = (13 - 5)/2
x1 = 8/2
x1 = 4
x2 = (13 + 5)/2
x2 = 18/2
x2 = 9

y1 = 13 - 4
y2 = 9
y2 = 13 - 9 
y2 = 4

Ответ: (4;9)  или (9;4)