(4d^2-4d+1)y=0

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Jul 03, 2024

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Solving the Equation (4d^2 - 4d + 1)y = 0

In this article, we will explore the solution to the equation (4d^2 - 4d + 1)y = 0. This is a quadratic equation in terms of d, and we will use various algebraic techniques to find the solutions.

Factoring the Equation

Let's start by trying to factor the equation:

(4d^2 - 4d + 1)y = 0

We can see that the left-hand side of the equation is a quadratic expression in terms of d. We can try to factor it as:

(2d - 1)^2*y = 0

This is a significant step, as we can now see that the equation is a product of two factors: (2d - 1)^2 and y.

Solving for y

From the factored form of the equation, we can see that either (2d - 1)^2 = 0 or y = 0.

Let's consider the first possibility: (2d - 1)^2 = 0. This implies that:

2d - 1 = 0

Solving for d, we get:

d = 1/2

Now, let's consider the second possibility: y = 0. This is a trivial solution, as it implies that the value of y is zero.

Conclusion

Therefore, the solutions to the equation (4d^2 - 4d + 1)y = 0 are:

• d = 1/2
• y = 0

These are the only possible solutions to the equation.