Ответ:
(-4;-4) (8;2)
Объяснение:
xy=16 ⇒ x≠0 y≠0
xy/(y+2)y + 4(y+2)y/xy = 4
16/(y+2)y + 4y(y+2)/16 = 4
16/(y+2)y + y(y+2)/4 = 4
(y+2)y=t
16/t + t/4 = 4
(64+t²-16t)/4t = 0
t²-16t+64=0 t≠0
(t-8)²=0 t=8
(y+2)y=8
y²+2y-8=0 y₁+y₂=-2 y₁y₂=-8 y₁=-4 y₂=2
y₁=-4 x₁=16/y₁=-4
y₂=2 x₂=16/2=8
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Ответ:
(-4;-4) (8;2)
Объяснение:
xy=16 ⇒ x≠0 y≠0
xy/(y+2)y + 4(y+2)y/xy = 4
16/(y+2)y + 4y(y+2)/16 = 4
16/(y+2)y + y(y+2)/4 = 4
(y+2)y=t
16/t + t/4 = 4
(64+t²-16t)/4t = 0
t²-16t+64=0 t≠0
(t-8)²=0 t=8
(y+2)y=8
y²+2y-8=0 y₁+y₂=-2 y₁y₂=-8 y₁=-4 y₂=2
y₁=-4 x₁=16/y₁=-4
y₂=2 x₂=16/2=8