Question

Dane są wielomiany u i w oraz f(x)=u(x)+2w(x), g(x)=2u(x)-3w(x)
Oblicz:
c) u(-1/2) i w(-1/2), gdy f(-1/2)=-9 i g(-1/2)=13

Answer 1

Niech u(-1/2)=a, w(-1/2)=b

 

a+2b=-9  /*(-2)

2a-3b=13

 

-2a-4b=18

 2a-3b=13

----------- +

     -7b=31 /:(-7)

      b=- 31/7=-4 i 3/7

a-62/7=-9

a=-9+8 i 6/7= -1/7

 

Odp. U(-1/2)=-1/7, W(-1/2)=-31/7

Answer 2

Należy rozwiązać układ równań:

f(-1/2)=u(-1/2)+2w(-1/2)

g(-1/2)=2u(x)-3w(-1/2)

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-9=u(-1/2)+2w(-1/2)

13=2u(-1/2)-3w(-1/2)

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u(-1/2)=-9-2w(-1/2)

13=2*(-9-2w(-1/2))-3w(-1/2)

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u(-1/2)=-9-2w(-1/2)

13=-18-4w(-1/2)-3w(-1/2)

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u(-1/2)=-9-2w(-1/2)

7w(-1/2)=-31

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u(-1/2)=-9-2w(-1/2)

w(-1/2)=-31/7

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u(-1/2)=-63/7 + 62/7

w(-1/2)=-31/7

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u(-1/2)=-1/7

w(-1/2)=-31/7