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Problem of the Day
If 
and 
, what is the value of 
?
A. 
B. 
C. 
D. 
E. Â 7
[latexpage]
$x\sqrt{12}+y\sqrt{51}=\sqrt{z}(2x+y\sqrt{17})$
On the left side, simplify $\sqrt{12}$ to $2\sqrt{3}$. Also, note that $\sqrt{51}$ can be written as $\sqrt{3}\sqrt{17}$. So the left side becomes $2x\sqrt{3}+y\sqrt{3}\sqrt{17}$. Now factor a $\sqrt{3}$ from the left side to get $\sqrt{3}(2x+y\sqrt{17})$. To make this match the right side, it must be true that $z=3$.