Question

对实数 $x$ ，定义 $\heartsuit(x)$ 为 $x$ 和 $x^2$ 的平均数。求的值。 $\heartsuit(1)+\heartsuit(2)+\heartsuit(3)?$

For a real number $x,$ define $\heartsuit(x)$ to be the average of $x$ and $x^2.$ What is $\heartsuit(1)+\heartsuit(2)+\heartsuit(3)?$

$3$

$6$

$10$

$12$

$20$

依次计算得以及 $\heartsuit(1) = \dfrac{1 + 1^2}{2} = 1,$ $\heartsuit(2) = \dfrac{2 + 2^2}{2} = 3,$ $\heartsuit(3) = \dfrac{3 + 3^2}{2} = 6.$

因此总和为 $1 + 3 + 6 = 10.$

所以正确答案是 C。

We have $\heartsuit(1) = \dfrac{1 + 1^2}{2} = 1,$ $\heartsuit(2) = \dfrac{2 + 2^2}{2} = 3,$ and $\heartsuit(3) = \dfrac{3 + 3^2}{2} = 6.$

Then $1 + 3 + 6 = 10.$

Thus, C is the correct answer.