Решить систему: x^2*y^3=16 y^2*x^3=2

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Решить систему:

x^2*y^3=16

y^2*x^3=2


Алгебра | 42 просмотров
Дано ответов: 2
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Правильный ответ

\left \{ {{x^2y^3=16\ \ \ (1)} \atop {y^2x^3=2\ \ \ (2)}} \right.

разделим  (1) на (2)

image\left \{ {y=8x} \atop {(8x)^2x^3=2}} \right.<=>\left \{ {y=8x} \atop {64x^5=2}} \right.<=>\left \{ {y=8x} \atop {x^5=\frac{2}{64}} \right.<=>\\\ \\\ <=>\left \{ {y=8x} \atop {x^5=\frac{1}{32}} \right.<=>\left \{ {y=8x} \atop {x=\frac{1}{2}} \right.<=>\left \{ {y=8*\frac{1}{2}} \atop {x=\frac{1}{2}} \right.<=>\left \{ {y=4}} \atop {x=\frac{1}{2}} \right." alt="\left \{ {{\frac{y}{x}=8} \atop {y^2x^3=2}} \right.<=>\left \{ {y=8x} \atop {(8x)^2x^3=2}} \right.<=>\left \{ {y=8x} \atop {64x^5=2}} \right.<=>\left \{ {y=8x} \atop {x^5=\frac{2}{64}} \right.<=>\\\ \\\ <=>\left \{ {y=8x} \atop {x^5=\frac{1}{32}} \right.<=>\left \{ {y=8x} \atop {x=\frac{1}{2}} \right.<=>\left \{ {y=8*\frac{1}{2}} \atop {x=\frac{1}{2}} \right.<=>\left \{ {y=4}} \atop {x=\frac{1}{2}} \right." align="absmiddle" class="latex-formula">

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x^2*y^3=16

y^2*x^3=2

 

y/x=8

y=8x

 

(8x)^2*x^3=2

 

64x^2*x^3=2

 

64x^5=2

 

32x^5=1

 

x^5=1/32

x=1/2

 

y=8*1/2=4

y=4

Ответ:(1/2,4)

 

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