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Math Help - functions

  1. #1
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    functions

    if f(x+2y,x-2y)=xy then f(x,y)=
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by prasum View Post
    if f(x+2y,x-2y)=xy then f(x,y)=

    Hint

    Use the substitution u=x+2y,v=x-2y .
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  3. #3
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    Quote Originally Posted by FernandoRevilla View Post
    Hint

    Use the substitution u=x+2y,v=x-2y .
    can yu please explain me the method
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Solving, x=(u+v)/2,\;y=(u-v)/4 so,

    f(u,v)=xy=\dfrac{u+v}{2}\cdot \dfrac{u-v}{4}=\dfrac{u^2-v^2}{8}

    Now, change the name of the variables, u by x and v by y.
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  5. #5
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    Quote Originally Posted by prasum View Post
    can yu please explain me the method
    You were told to let u= x+ 2y, v= x- 2y. The point of that is that f(x+ 2y, x- 2y)= xy becomes f(u, v)= xy. Now you want to write xy in terms of u and v. Can you solve u= x+ 2y and v= x- 2y for x and y in terms of u and v?
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