Question

对实数 $x$ 和 $y$ ，定义 $x \spadesuit y = (x+y)(x-y)$ 。求 $3 \spadesuit (4 \spadesuit 5)$ 的值。

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

$-72$

$-27$

$-24$

$24$

$72$

先计算内层运算 $4 \spadesuit 5$ 。

Evaluate the inner operation $4 \spadesuit 5$ first

$x \spadesuit y = x^2 - y^2$ 。

$x \spadesuit y = x^2 - y^2$

因为 $x \spadesuit y = (x+y)(x-y) = x^2 - y^2$ ，所以 $4 \spadesuit 5 = 16 - 25 = -9$ 。

接着 $3 \spadesuit (-9) = 9 - 81 = -72$ 。

所以正确答案是 A。

Since $x \spadesuit y = (x+y)(x-y) = x^2 - y^2,$ we have $4 \spadesuit 5 = 16 - 25 = -9.$

Then $3 \spadesuit (-9) = 9 - 81 = -72.$

Thus, the correct answer is A.