Question

Решите систему уравнений

$left { {{x^3y+xy^3=300} atop {x^2+y^2=25}} right.$

Answer 1

xy*(x²+y²)=300

xy*25=300

xy=12

x=12/y

(12/y)²+y²=25

144/y²+y²=25

(y²)²-25y²+144=0

D=25²-4*144=49=7²

(1)  y²1=(25+7)/2=16

(2)  y²2=(25-7)/2=9

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Из (1):

y1 = 4       x1 = 12/4 = 3

y2 = -4     x2 = 12/(-4) = -3

Из (2):

y3 = 3      x3 = 12/3 = 4

y4 = -3      x4 = 12/(-3) = -4