carcass wrote:
The number \(\sqrt{63-36\sqrt{3}}\) can be expressed as \(x + y \sqrt{3}\) for some integers x and y. What is the value of xy ?
A. –18
B. –6
C. 6
D. 18
E. 27
Here is what comes to my mind when I see this question:
\(\sqrt{63-36\sqrt{3}} = x + y \sqrt{3}\)
Now, this is a PS question so I will have a unique value for xy. All I need to do is find one set of values which satisfy this equation.
There is nothing I can compare while there is the sqrt on the left hand side. So let's square both sides.
\(63 - 36\sqrt{3} = x^2 + 3y^2 + 2xy\sqrt{3}\)
The co-efficient of the irrational term has to be equal to on both sides. So
-36 = 2xy
xy = -18
Answer (A)
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