`25=(ky-1)^2`
In the equation above y=-2 is one solution. If K is a constant, what is a possible value of k?

Options

A. -13
B. -3
C. 0
D. 5

Answer

To solve the equation \( 25 = (ky - 1)^2 \) given that \( y = -2 \) is one solution, we can follow these steps:

### Step 1: Substitute \( y = -2 \) into the equation
We start by substituting \( y = -2 \) into the equation:

\[ 25 = (k(-2) - 1)^2 \]

### Step 2: Simplify the equation
This simplifies to:

\[ 25 = (-2k - 1)^2 \]

### Step 3: Take the square root of both sides
Taking the square root of both sides, we have:

\[ \sqrt{25} = | -2k - 1 | \]

This gives us two cases to consider:

1. \( -2k - 1 = 5 \)
2. \( -2k - 1 = -5 \)

### Step 4: Solve the first case
For the first case:

\[ -2k - 1 = 5 \]

Adding 1 to both sides:

\[ -2k = 6 \]

Dividing by -2:

\[ k = -3 \]

### Step 5: Solve the second case
For the second case:

\[ -2k - 1 = -5 \]

Adding 1 to both sides:

\[ -2k = -4 \]

Dividing by -2:

\[ k = 2 \]

### Step 6: Identify possible values of \( k \)
We have found two possible values for \( k \):

1. \( k = -3 \)
2. \( k = 2 \)

### Step 7: Determine which value is in the options
The options provided are -13, -3, 0, and 5. Among these, the value \( k = -3 \) is present.

### Conclusion
Thus, a possible value of \( k \) is:

\[ \boxed{-3} \]