### Smallest value

Posted:

**Sun Jan 29, 2012 9:38 pm**Find the smallest value of:

$|x^2-8xy+9y^2-16y+10|$ for $x,y \in R$

$|x^2-8xy+9y^2-16y+10|$ for $x,y \in R$

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Posted: **Sun Jan 29, 2012 9:38 pm**

Find the smallest value of:

$|x^2-8xy+9y^2-16y+10|$ for $x,y \in R$

$|x^2-8xy+9y^2-16y+10|$ for $x,y \in R$

Posted: **Sun Jan 29, 2012 10:08 pm**

Isn't there a typo? Header says highest and problem says lowest.

Posted: **Sun Jan 29, 2012 10:33 pm**

Opppssss.... .Thanks..

Posted: **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 $0$.

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 $0$.