Sequence And Series Question 529
Question: If $ f(x+y,x-y)=xy,, $ then the arithmetic mean of $ f(x,y) $ and $ f(y,x) $ is
[AMU 2002, 05]
Options:
A) $ x $
B) $ y $
C) 0
D) 1
Show Answer
Answer:
Correct Answer: C
Solution:
Let $ x+y=u,x-y=v $
Þ $ x=\frac{u+v}{2},y=\frac{u-v}{2} $ ,
$ \therefore f(u,v)=( \frac{u+v}{2} ).( \frac{u-v}{2} ) $ Now, $ \frac{f(x,y)+f(y,x)}{2}=\frac{( \frac{x+y}{2}.\frac{x-y}{2} )+( \frac{y+x}{2}.\frac{y-x}{2} )}{2}=0 $
BETA
