Question

Y^2= | 3n | ; Find K(-2)
Answer should be +- square root of 6

Answer 1

To find \( K(-2) \) from the equation \( Y^2 = |3n| \), we can interpret the equation in terms of variables.

Let's set \( n = -2 \):

\[
Y^2 = |3(-2)|
\]

Calculating this gives:

\[
Y^2 = |-6| = 6
\]

Now, taking the square root of both sides:

\[
Y = \pm \sqrt{6}
\]

Thus, for \( K(-2) \):

\[
K(-2) = \pm \sqrt{6}
\]

Therefore, the answer is:

\[
\boxed{\pm \sqrt{6}}
\]

Answer 2

So Y^2 = give sus |-6| how did it become a positive 6?

Answer 3

Let's clarify how the absolute value works in this context.

The equation you provided is:

\[
Y^2 = |3n|
\]

When you substitute \(n = -2\):

\[
Y^2 = |3(-2)|
\]

Calculating the inside of the absolute value:

\[
3(-2) = -6
\]

Now, we need to take the absolute value of \(-6\):

\[
| -6 | = 6
\]

So, you have:

\[
Y^2 = 6
\]

Taking the square root of both sides, we find:

\[
Y = \pm \sqrt{6}
\]

As a result, when we plug in \(n = -2\), the absolute value changes \(-6\) to \(6\), which is why we ended up with:

\[
K(-2) = \pm \sqrt{6}
\]

I hope this clears up any confusion! The correct interpretation of the absolute value made all the difference.

Answer 4

Oh ok so it’s because it became square root of -6 that it became a positive 6 right?

Answer 5

Actually, let's clarify that point. The absolute value operation does not depend on taking the square root; it specifically deals with ensuring that the quantity is non-negative.

Here's the breakdown again:

1. When you compute \(3n\) with \(n = -2\):
\[
3(-2) = -6
\]

2. The absolute value of \(-6\) is:
\[
| -6 | = 6
\]

3. Thus, when we substitute back into the equation \(Y^2 = |3n|\), we get:
\[
Y^2 = 6
\]

4. Now when you take the square root:
\[
Y = \pm \sqrt{6}
\]

The important point is that the absolute value function converts negative numbers to positive. The operation of taking the square root applies to the non-negative result of the absolute value.

So, it’s not that \(Y^2\) becomes the square root of \(-6\)—in fact, that would be invalid in the real number domain (since \(\sqrt{-6}\) is not a real number). Instead, it’s the absolute value that ensures the result is \(6\), a non-negative quantity, which you then take the square root of. Thus, the final result remains:

\[
K(-2) = \pm \sqrt{6}
\]

So to summarize, the absolute value changes the negative number \(-6\) to the positive number \(6\), and then you take the square root of \(6\) to get your results.