Решить систему уравнений

x+y=13

√x+√y=5

V x = a; V y = b; Х > = 0; y > = 0

a + b = 5

a = 5 - b

(5 - b) ^2 + b^2 = 13

25 - 10b + b^2 + b^2 = 13

2b^2 - 10b + 12 = 0

2 (b^2 - 5b + 6) = 0

D = 25 - 24 = 1

b1 = (5 + 1) : 2 = 3

b2 = (5 - 1) : 2 = 2

a1 = 5 - 3 = 2

a2 = 5 - 2 = 3

V x = a

V x = 2

X1 = 4

V x = 3

X2 = 9

V y = b

V y = 3

y1 = 9

V y = 2

y2 = 4

Ответ (4; 9) ; (9; 4)