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)