Question

Решить систему: x^2*y^3=16 y^2*x^3=2

Answer 1

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

разделим  (1) на (2)

$\left \{ {{\frac{y}{x}=8} \atop {y^2x^3=2}} \right.<=\left \{ {y=8x} \atop {(8x)^2x^3=2}} \right.<=\left \{ {y=8x} \atop {64x^5=2}} \right.<=\left \{ {y=8x} \atop {x^5=\frac{2}{64}} \right.<=\\\ \\\ <=\left \{ {y=8x} \atop {x^5=\frac{1}{32}} \right.<=\left \{ {y=8x} \atop {x=\frac{1}{2}} \right.<=\left \{ {y=8*\frac{1}{2}} \atop {x=\frac{1}{2}} \right.<=\left \{ {y=4}} \atop {x=\frac{1}{2}} \right.$

Answer 2

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)