Smallest value

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sourav das
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Smallest value

Unread post by sourav das » Sun Jan 29, 2012 9:38 pm

Find the smallest value of:
$|x^2-8xy+9y^2-16y+10|$ for $x,y \in R$
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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*Mahi*
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Re: Highest value

Unread post by *Mahi* » Sun Jan 29, 2012 10:08 pm

Isn't there a typo? Header says highest and problem says lowest.
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sourav das
Posts: 461
Joined: Wed Dec 15, 2010 10:05 am
Location: Dhaka
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Re: Smallest value

Unread post by sourav das » Sun Jan 29, 2012 10:33 pm

Opppssss.... .Thanks..
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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*Mahi*
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Re: Smallest value

Unread post by *Mahi* » Mon Jan 30, 2012 1:03 pm

\[0\]
The expression is \[|(x-4y)^2-(\sqrt {7} y+\frac{8}{\sqrt{7}})^2+\frac{134}{7}|\] and setting $x=4y$, $y=\frac 17 (\sqrt{134}-8),\frac 17 (-\sqrt{134}-8)$ gives us $0$.
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