Test of Mathematics Solution Subjective 33 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.
Also see: Cheenta I.S.I. & C.M.I. Entrance Course
Let be a fixed odd positive integer. Find the minimum value of
, where
are non-negative integers and
.
We have . Therefore we get an equation in
where
is a constant, precisely
.
To minimise, we differentiate w.r.t
.
So (for minimum
)
That gives us .
But the question tell us that is odd and
is an integer. therefore we have to take the closest possible integer value to
, which is
and
.
As already defined, taking to be any one of the above
automatically takes the other value.
Therefore the minimum value of is given by
.
Test of Mathematics Solution Subjective 33 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.
Also see: Cheenta I.S.I. & C.M.I. Entrance Course
Let be a fixed odd positive integer. Find the minimum value of
, where
are non-negative integers and
.
We have . Therefore we get an equation in
where
is a constant, precisely
.
To minimise, we differentiate w.r.t
.
So (for minimum
)
That gives us .
But the question tell us that is odd and
is an integer. therefore we have to take the closest possible integer value to
, which is
and
.
As already defined, taking to be any one of the above
automatically takes the other value.
Therefore the minimum value of is given by
.