(x+sqrt{5})(1+sqrt{5})=sqrt{5}
x * (1+sqrt{5}) + sqrt{5} * (1+sqrt{5}) = sqrt{5}
x + x * sqrt{5} + sqrt{5} + sqrt{5} * sqrt{5} = sqrt{5}
x + x * sqrt{5} + sqrt{5} + 5 = sqrt{5}
x + x * sqrt{5} + 5 = 0
x * (1 + sqrt{5}) = -5
x = ( -5 ) / (1 + sqrt{5})
Możemy teraz usunąć niewymierność z mianownika:
x = ( -5 ) / (1 + sqrt{5}) = [ -5 * (1 - sqrt{5}) ] / [(1 + sqrt{5}) * (1 - sqrt{5})] = ( -5 + 5 * sqrt{5}) / (1 - 5) =
( -5 + 5 * sqrt{5}) / (- 4) = ( 5 - 5 * sqrt{5}) / 4
