Prove that the equation x ^ 2-4x + 5 = 0 is equivalent to the equation 3 + 2 * | 1-2x | = 0

If the equations have the same set of roots, then they are considered equivalent. If the equations have no roots, then they are also equivalent.

Let’s solve the quadratic equation:

x ^ 2 – 4 * x + 5 = 0.

D = (-4) ^ 2 – 4 * 1 * 5 = 16 – 20 = -4.

If the discriminant is negative, then the equation will have no roots.

Let’s solve the second equation:

3 + 2 * | 1 – 2 * x | = 0.

Since the sum is equal to 0 and 3> 0, the expression 2 * | 1 – 2 * x | must be negative, but this cannot be, therefore the equation has no roots.

Equivalence has been proven.