Question

Решить систему уравнений x+y=13 √x+√y=5

Answer 1

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 )