help algebra

Pull over terms to the left side:

4x²-4x+1=0

Factor:

(2x-1)²=0

a would be 1/2. b would also be 1/2.

1/a + 1/b would be 4.

Simplify the equation to: $4x^2-4x+1=0$

We can rewrite ${1 \over a} + {1 \over b}$ as ${b+a} \over {ab}$

Using Vieta's, the sum of the roots (a+b) is $-b \over a$ and the product (ab) is $c \over a$

This means that the sum of the roots is ${4 \over 4} = 1$, and that the product of the roots is $1 \over 4$

Substituting this in, we find that $\large{{1 \over a} + {1 \over b} = {1 \over {1 \over 4}} = \color{brown}\boxed{4}}$