The roots of the equations `(x+3)(x-3)=160` are

Options

A. `+-13`
B. `13,13`
C. `+-12`
D. `12,12`

Answer

To find the roots of the equation \((x+3)(x-3) = 160\), we can follow these steps:

### Step 1: Expand the left side of the equation
We start with the equation:
\[ (x+3)(x-3) = 160 \]
Using the difference of squares formula, we can expand the left side:
\[ x^2 - 9 = 160 \]

### Step 2: Rearrange the equation
Next, we rearrange the equation to set it to zero:
\[ x^2 - 9 - 160 = 0 \]
This simplifies to:
\[ x^2 - 169 = 0 \]

### Step 3: Factor the quadratic equation
Now, we can factor the equation:
\[ x^2 - 169 = (x - 13)(x + 13) = 0 \]

### Step 4: Set each factor to zero
To find the roots, we set each factor equal to zero:
1. \(x - 13 = 0\)
2. \(x + 13 = 0\)

### Step 5: Solve for \(x\)
Solving these equations gives us:
1. \(x = 13\)
2. \(x = -13\)

### Conclusion
The roots of the equation \((x+3)(x-3) = 160\) are:
\[ x = 13 \quad \text{and} \quad x = -13 \]