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.