The sum of a number and 3 is equal to the positive square root of 12 times the number. Find the number.

Question

Quizplus · Accepted Answer

Let's call the number we're looking for "x." The problem tells us that the sum of x and 3 is equal to the positive square root of 12 times x. We can write this as an equation:

x + 3 = sqrt(12x)

To solve for x, we'll start by squaring both sides of the equation:

(x + 3)^2 = 12x

Expanding the left side of the equation, we get:

x^2 + 6x + 9 = 12x

Moving all the terms to one side of the equation, we get:

x^2 - 6x - 9 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = -6, and c = -9. Plugging in these values, we get:

x = (6 ± sqrt(36 + 36)) / 2

Simplifying under the square root, we get:

x = (6 ± 6) / 2

So x = 3 or x = 9/2. Both of these values satisfy the original equation, but we're asked to find a positive integer, so the answer is x = 3. Therefore, the best choice is C, 3.

The Sum of a Number and 3 Is Equal to the Positive