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sazhenkova99
@sazhenkova99
July 2022
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Решите систему уравнений
X² + y² =10
xy = 3
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selmash21
Х=3/у
(3/у)^2+у^2=10
9/у^2 +у^2=10
9+у^4=10у^2
у^4-10у^2+9=0
у^2=а
д=100-4×9=64
а1=(10-8)/2=1
а2=(10+8)/2=9
у^2=1
у1=1
у2=-1
у^2=9
у3=3
у4=-3
х1=3/1=3
х2=3/(-1)=-3
х3=3/3=1
х4=3/(-3)=-1
(3;1) (-3;-1) (1;3) (-1;-3)
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Answers & Comments
(3/у)^2+у^2=10
9/у^2 +у^2=10
9+у^4=10у^2
у^4-10у^2+9=0
у^2=а
д=100-4×9=64
а1=(10-8)/2=1
а2=(10+8)/2=9
у^2=1
у1=1
у2=-1
у^2=9
у3=3
у4=-3
х1=3/1=3
х2=3/(-1)=-3
х3=3/3=1
х4=3/(-3)=-1
(3;1) (-3;-1) (1;3) (-1;-3)