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JEE Main & Advanced Mathematics Sequence & Series Question Bank Arithmetic Progression

  • question_answer
    If \[f(x+y,x-y)=xy\,,\] then the arithmetic mean of \[f(x,y)\] and \[f(y,x)\] is [AMU 2002, 05]

    A) \[x\]

    B) \[y\]

    C) 0

    D) 1

    Correct Answer: C

    Solution :

    Let \[x+y=u,\,\,x-y=v\] Þ \[x=\frac{u+v}{2},y=\frac{u-v}{2}\],\[\therefore f(u,v)=\left( \frac{u+v}{2} \right).\left( \frac{u-v}{2} \right)\] Now,\[\frac{f(x,y)+f(y,x)}{2}=\frac{\left( \frac{x+y}{2}.\frac{x-y}{2} \right)+\left( \frac{y+x}{2}.\frac{y-x}{2} \right)}{2}=0\]


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