Question

Para un número real

x,

define

\heartsuit(x)

como el promedio de

x

y

x^2.

¿Cuál es el valor de la siguiente expresión?

\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 the value of the following expression?

\heartsuit(1)+\heartsuit(2)+\heartsuit(3)

3

6

10

12

20

Calcula por separado

\heartsuit(1),\heartsuit(2),\heartsuit(3)

.

Evaluate

\heartsuit(1),\heartsuit(2),\heartsuit(3)

separately

\heartsuit(x)=\dfrac{x+x^2}{2}

.

\heartsuit(x)=\dfrac{x+x^2}{2}

Tenemos

\heartsuit(1) = \dfrac{1 + 1^2}{2} = 1,

\heartsuit(2) = \dfrac{2 + 2^2}{2} = 3,

y

\heartsuit(3) = \dfrac{3 + 3^2}{2} = 6.

Entonces

1 + 3 + 6 = 10.

Por lo tanto, C es la respuesta correcta.

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.