Understanding the Equation

The given equation is (l - m/2)x^2 - (l m/2)x + m = 0. We need to find the values of x that satisfy this equation. To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a),

where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.

Applying the Quadratic Formula

In this equation, a = (l - m/2), b = -(l m/2), and c = m. Let's substitute these values into the quadratic formula and simplify the equation step by step.

x = (-(l m/2) ± √((l m/2)^2 - 4(l - m/2)m)) / (2(l - m/2)),

Simplifying further:

x = (-(l m/2) ± √((l^2 m^2)/4 - 4lm + 2m^2)) / (2(l - m/2)),

x = (-lm ± √((l^2 m^2 - 16lm + 8m^2)) / (2l - m)).

Discriminant of the Quadratic Formula

To determine the number of solutions, we need to analyze the discriminant of the quadratic formula, which is the expression inside the square root, (l^2 m^2 - 16lm + 8m^2).

Case 1: Discriminant > 0
If the discriminant is greater than zero, i.e., (l^2 m^2 - 16lm + 8m^2) > 0, then there are two distinct real solutions for x.

Case 2: Discriminant = 0
If the discriminant is equal to zero, i.e., (l^2 m^2 - 16lm + 8m^2) = 0, then there is one real solution for x.

Case 3: Discriminant < />
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Conclusion

In conclusion, the number of values of x that satisfy the given equation depends on the discriminant, (l^2 m^2 - 16lm + 8m^2). If the discriminant is greater than zero, there are two distinct real solutions. If the discriminant is equal to zero, there is one real solution. If the discriminant is less than zero, there are no real solutions.

Very easy but i don't know the answer