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 \(\large{{1 \over a} + {1 \over b} = {1 \over {1 \over 4}} = \color{brown}\boxed{4}}\)