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Smallest value
Posted: Sun Jan 29, 2012 9:38 pm
by sourav das
Find the smallest value of:
$|x^2-8xy+9y^2-16y+10|$ for $x,y \in R$
Re: Highest value
Posted: Sun Jan 29, 2012 10:08 pm
by *Mahi*
Isn't there a typo? Header says highest and problem says lowest.
Re: Smallest value
Posted: Sun Jan 29, 2012 10:33 pm
by sourav das
Opppssss.... .Thanks..
Re: Smallest value
Posted: Mon Jan 30, 2012 1:03 pm
by *Mahi*
\[0\]
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 $0$.