If the sum of the slopes of the lines given by `x^2-2c x y-7y^2=0` is four times their product, then the value of `c` is_____

Explanation

To solve the problem, we need to find the value of \( c \) given the equation of the pair of straight lines \( x^2 - 2cxy - 7y^2 = 0 \). We know that the sum of the slopes of the lines is four times their product.

### Step-by-Step Solution:

1. **Identify the coefficients**:
The general form of a pair of straight lines is given by \( ax^2 + 2hxy + by^2 = 0 \). For our equation:
\[
a = 1, \quad h = -c, \quad b = -7
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