If f(x + y,x - y) = xy,, then arithmetic mean of f(x,y) and f(y,x) is

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8. Sequences and Series

medium

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

$x$

$y$

$0$

$1$

Solution

==> $x = \frac{{u + v}}{2},y = \frac{{u – v}}{2}$,

$\therefore f(u,v) = \left( {\frac{{u + v}}{2}} \right).\left( {\frac{{u – v}}{2}} \right)$

Now,$\frac{{f(x,y) + f(y,x)}}{2} = \frac{{\left( {\frac{{x + y}}{2}.\frac{{x – y}}{2}} \right) + \left( {\frac{{y + x}}{2}.\frac{{y – x}}{2}} \right)}}{2} = 0$.

Standard 11

Mathematics

If ${a_1},\;{a_2},\,{a_3},……{a_{24}}$ are in arithmetic progression and ${a_1} + {a_5} + {a_{10}} + {a_{15}} + {a_{20}} + {a_{24}} = 225$, then ${a_1} + {a_2} + {a_3} + …….. + {a_{23}} + {a_{24}} = $

medium

If $a _{1}, a _{2}, a _{3} \ldots$ and $b _{1}, b _{2}, b _{3} \ldots$ are $A.P.$ and $a_{1}=2, a_{10}=3, a_{1} b_{1}=1=a_{10} b_{10}$ then $a_{4} b_{4}$ is equal to

medium

(JEE MAIN-2022)

If the sum of the first $n$ terms of the series $\sqrt 3 + \sqrt {75} + \sqrt {243} + \sqrt {507} + ……$ is $435\sqrt 3 $ , then $n$ equals

hard

(JEE MAIN-2017)

The four arithmetic means between $3$ and $23$ are

easy

The sum of all the elements in the set $\{\mathrm{n} \in\{1,2, \ldots \ldots ., 100\} \mid$ $H.C.F.$ of $n$ and $2040$ is $1\,\}$ is equal to $…..$

hard

(JEE MAIN-2021)

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

Solution

Similar Questions

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