`sqrt(x^(2)-9x+20)-sqrt(x^(2)-12x+32)=sqrt(2x^(2)-25x+68)`:

Options

A. 4, 9
B. 3, 9
C. 2, 4
D. 2, 6

Answer

To solve the equation

\[ \sqrt{x^2 - 9x + 20} - \sqrt{x^2 - 12x + 32} = \sqrt{2x^2 - 25x + 68} \]

we will follow these steps:

### Step 1: Simplify the expressions under the square roots.

1. **First expression:**
\[ x^2 - 9x + 20 = (x - 4)(x - 5) \]
2. **Second expression:**
\[ x^2 - 12x + 32 = (x - 4)(x - 8) \]
3. **Third expression:**
\[ 2x^2 - 25x + 68 = 2(x^2 - \frac{25}{2}x + 34) \]