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vladrus113
@vladrus113
July 2022
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Решите, пожалуйста, систему уравнений.
[tex] \left \{ {{ x^{2} - 4xy +4 y^{2} = 2x-4y+3} \atop { \sqrt{3x-6y} =2-xy}} \right. [/tex].
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sedinalana
Verified answer
1)(x-2y)²-2(x-2y)-3=0
x-2y=a
a²-2a-3=0
a1+a2=2 U a1*a2=-3
a1=-1 U a2=3
2)
а)x-2y=-1
√[3(x-2y)]=2-xy
2-xy=√-3 нет решения
б)x-2y=3
2-xy=3
xy=-1
x=3+2y
(3+2y)y=-1
2y²+3y+1=0
D=9-8=1
y1=(-3-1)/4=-1⇒x1=3-2=1
y2=(-3+10/4=-0,5⇒x2=3-1=2
Ответ (1;-1);(2;-0,5)
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Answers & Comments
Verified answer
1)(x-2y)²-2(x-2y)-3=0x-2y=a
a²-2a-3=0
a1+a2=2 U a1*a2=-3
a1=-1 U a2=3
2)
а)x-2y=-1
√[3(x-2y)]=2-xy
2-xy=√-3 нет решения
б)x-2y=3
2-xy=3
xy=-1
x=3+2y
(3+2y)y=-1
2y²+3y+1=0
D=9-8=1
y1=(-3-1)/4=-1⇒x1=3-2=1
y2=(-3+10/4=-0,5⇒x2=3-1=2
Ответ (1;-1);(2;-0,5)