Finding A and B with (E)... 4x² + (2√2 - 2)x - √2 = 0

Question

(E)... 4x² + (2√2 - 2)x - √2 = 0

We need to calculate A and B without Calculating x1 and x2 from (E)

A = (1/x1²) + (1/x2²)

B = (1/x2-1) + (1/x1-1)

Answer 1

x² + (√2/2 - 1/2)x - √2/4 = 0.

From here by Veet's Theorem x₁ = 1/2, x₂ = - √2/2.

A = 2² + 2 = 6;

B = (- √2 - 1) + (2 - 1) = - √2