# Problem of the Day

If and , what is the value of ?

A.

B.

C.

D.

E. Â 7

### Solution

[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 $z=3$.

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