CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

If $$f\left( x+y,\  x-y \right) =xy$$, then the arithmetic mean of $$f(x,y)$$ and $$f(y,x)$$ is


Solution

Given: $$f\left( x+y,x-y \right) =xy$$

Replacing $$x$$ by $$\dfrac { x+y }{ 2 } $$ and $$y$$ by $$\dfrac { x-y }{ 2 } $$

Gives $$f\left( x,y \right) =\dfrac { { x }^{ 2 }-{ y }^{ 2 } }{ 4 } $$

Now the arithmetic mean is $$\dfrac { f\left( x,y \right) +f\left( y,x \right)  }{ 2 } =\dfrac { \dfrac { { x }^{ 2 }-{ y }^{ 2 } }{ 4 } +\dfrac { { y }^{ 2 }-{ x }^{ 2 } }{ 4 }  }{ 2 } =0$$

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image