Exercise-1.14(new book) (BOMC-2011)

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*Mahi*
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Re: Exercise-1.14(new book) (BOMC-2011)

Unread post by *Mahi* » Mon Oct 31, 2011 8:21 pm

sourav das wrote:$4n^2$ is just smaller than $4n^2 + n$
So let $\sqrt{4n^2 + n}=2n + x $ here x is the fractional part. then do it in your way.
But I think this is easier(no squaring etc.)
$\sqrt {4n^2}< \sqrt {4n^2+n}<\sqrt {4n^2+n+1}$
Or $2n< \sqrt {4n^2+n}<2n+\frac 1 4$
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Re: Exercise-1.14(new book) (BOMC-2011)

Unread post by sourav das » Mon Oct 31, 2011 8:23 pm

আমি তো শুধু বলসিলাম যেকোনো আক্তা দিয়াই হবে।
You spin my head right round right round,
When you go down, when you go down down......
(-$from$ "$THE$ $UGLY$ $TRUTH$" )

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Re: Exercise-1.14(new book) (BOMC-2011)

Unread post by *Mahi* » Mon Oct 31, 2011 8:28 pm

Seems like two inequalities cut the time in half.
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Re: Exercise-1.14(new book) (BOMC-2011)

Unread post by sourav das » Mon Oct 31, 2011 8:34 pm

If you're saying about cut one minute to 30 second, yes you're right. But it is always better to have and know different ideas. Only for this reason i said so. It may help everyone with more choices.
You spin my head right round right round,
When you go down, when you go down down......
(-$from$ "$THE$ $UGLY$ $TRUTH$" )

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Re: Exercise-1.14(new book) (BOMC-2011)

Unread post by *Mahi* » Mon Oct 31, 2011 8:42 pm

sourav das wrote:If you're saying about cut one minute to 30 second, yes you're right. But it is always better to have and know different ideas. Only for this reason i said so. It may help everyone with more choices.
Yes , I agree, everybody ought to know all the solutions of the basic level problems.
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Re: Exercise-1.14(new book) (BOMC-2011)

Unread post by sourav das » Mon Oct 31, 2011 8:46 pm

*Mahi* wrote:
sourav das wrote:If you're saying about cut one minute to 30 second, yes you're right. But it is always better to have and know different ideas. Only for this reason i said so. It may help everyone with more choices.
Yes , I agree, everybody ought to know all the solutions of the basic level problems.
I also agree with you.
You spin my head right round right round,
When you go down, when you go down down......
(-$from$ "$THE$ $UGLY$ $TRUTH$" )

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Re: Exercise-1.14(new book) (BOMC-2011)

Unread post by Ashfaq Uday » Mon Nov 07, 2011 6:42 am

\[\left \lfloor \sqrt{\left ( 4n^2+n \right )} \right \rfloor=2n\]
which leads us to \[n< \left ( n+\left ( 1/16 \right ) \right )\]and its obvious. :D

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