Решите систему уравнений
[tex]\left \{ {{x^3y+xy^3=300} \atop {x^2+y^2=25}} \right.[/tex]
[tex]\left \{ {{x^3y+xy^3=300} \atop {x^2+y^2=25}} \right.[/tex]
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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