i cant find the way find x+1/x if x2-4x-1= 0

Question

The ans is 2√5. Pls help me find the ans

Answer 1

Solve the quadratic equation for x (either by completing the square or using the quadratic formula):

x = (-b (+ or -)  sqrt(b*b-4*a*c))/(2*a)

So,

x = 2 + sqrt(5) or x = 2-sqrt(5)

Then use algebra to find 1/x = 1/(2+sqrt(5)) which if we multiply the numerator and denominator by the conjugate (2-sqrt(5)) and simplify we get 1/x = (2-sqrt(5))/(-1).   If we picked the other solution of the quadratic formula and found 1/x we would get (2+sqrt(5))/(-1).

So, either way when we add x and 1/x we get 2*sqrt(5).