Find the quadratic equation with rational coefficients whose one root is `1//(2+sqrt(5))dot`

Explanation

If the coefficients are rational, then irrational roots occur in conjugate pair. Given that if one root is `alpha = 1//(2 + sqrt(5)) = sqrt(5)-2,`
then the other root is `beta = 1//(2 - sqrt(5)) = -(2 + sqrt(5)).`
Sum of roots ` alpha + beta = -4` and product of roots `alpha beta = - 1` .Thus required equation is `x^(2) + 4x - 1 = 0`