The pair of lines represented by the equation 5x^2 + 6xy + 2y^2 = 0 has:

The pair of lines represented by the equation 5x^2 + 6xy + 2y^2 = 0 has:

Step 1: Identify the equation given, which is 5x^2 + 6xy + 2y^2 = 0.
Step 2: Recognize that this is a quadratic equation in terms of x and y.
Step 3: The general form of a quadratic equation is Ax^2 + Bxy + Cy^2 = 0, where A = 5, B = 6, and C = 2.
Step 4: Calculate the discriminant using the formula D = B^2 - 4AC.
Step 5: Substitute the values: D = (6)^2 - 4(5)(2).
Step 6: Calculate D = 36 - 40 = -4.
Step 7: Since the discriminant D is negative, it indicates that there are no real roots.
Step 8: Therefore, the pair of lines represented by the equation does not exist in the real number system.

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