Помогите решить Систему уравнений в падробнастях
[tex] \left \{ {{2(x+y)=10,6} \atop {x*y=6,72}} \right. [/tex]
[tex] \left \{ {{x+y=3} \atop {x^{2}+y^{2} =65}} \right. [/tex]
[tex] \left \{ {{2(x+y)=10,6} \atop {x*y=6,72}} \right. [/tex]
[tex] \left \{ {{x+y=3} \atop {x^{2}+y^{2} =65}} \right. [/tex]
Answers & Comments
{ xy=6.72
{x+y=5.3
{xy=6.72
x=5.3-y
(5.3-y)y=6.72
5.3y-y²=6.72
-y²+5.3y-6.72=0
y²-5.3y+6.72=0
D=5.3²-4*6.72=28.09-26.88=1.21
y₁=5.3-1.1=2.1 x₁=5.3-2.1
2 x₁=3.2
y₂=5.3+1.1=3.2 x₂=5.3-3.2
2 x₂=2.1
Ответ: х=3,2 у=2,1
х=2,1 у=3,2
2) {x+y=3
{x²+y²=65
x+y=3
x=3-y
(3-y)²+y²=65
9-6y+y²+y²-65=0
2y²-6y-56=0
y²-3y-28=0
D=9+4*28=9+112=121
y₁=3-11=-4 x₁=3-(-4)
2 x₁=7
y₂=3+11=7 x₂=3-7
2 x₂=-4
Ответ: х=7 у=-4
х=-4 у=7