Difference between revisions of "2006 AMC 12B Problems/Problem 2"

Revision as of 13:57, 13 November 2007

For real numbers $x$ and $y$ , define $x\spadesuit y = (x + y)(x - y)$ . What is $3\spadesuit(4\spadesuit 5)$ ?

$\text {(A) } - 72 \qquad \text {(B) } - 27 \qquad \text {(C) } - 24 \qquad \text {(D) } 24 \qquad \text {(E) } 72$

$4\spadesuit 5=-9$

$3\spadesuit -9=-72 \Rightarrow \text{(B)}$

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 == Problem ==
+For real numbers <math>x</math> and <math>y</math>, define <math>x\spadesuit y = (x + y)(x - y)</math>.  What is <math>3\spadesuit(4\spadesuit 5)</math>?
+<math>\text {(A) } - 72 \qquad \text {(B) } - 27 \qquad \text {(C) } - 24 \qquad \text {(D) } 24 \qquad \text {(E) } 72</math>
 == Solution ==
+<math>4\spadesuit 5=-9</math>
+<math>3\spadesuit -9=-72 \Rightarrow \text{(B)}</math>
 == See also ==
 * [[2006 AMC 12B Problems]]