if f(x+2y,x-2y)=xy then f(x,y)=
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Originally Posted by prasum if f(x+2y,x-2y)=xy then f(x,y)= Hint Use the substitution $\displaystyle u=x+2y,v=x-2y$ .
Originally Posted by FernandoRevilla Hint Use the substitution $\displaystyle u=x+2y,v=x-2y$ . can yu please explain me the method
Solving, $\displaystyle x=(u+v)/2,\;y=(u-v)/4$ so, $\displaystyle f(u,v)=xy=\dfrac{u+v}{2}\cdot \dfrac{u-v}{4}=\dfrac{u^2-v^2}{8}$ Now, change the name of the variables, $\displaystyle u$ by $\displaystyle x$ and $\displaystyle v$ by $\displaystyle y$.
Originally Posted by prasum 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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