[tex]\\x+\sqrt5+x\sqrt5=1 \\x(1+\sqrt5)=1-\sqrt5/:(1+\sqrt5) \\x=\frac{(1-\sqrt5)^2}{(1+\sqrt5)(1-\sqrt5)}=\frac{1-2\sqrt5+5}{1-5} \\x=\frac{6-2\sqrt5}{-4} \\x=\frac{\sqrt5-3}{2}[/tex]
x + (1 + x)*√5 = 1
x + √5 + √5*x = 1
x(1 + √5) = 1 - √5 /:(1+√5
x = (1-√5)/(1+√5) * (1-√5/(1-√5)
x = (1-√5)²/(1-5)
x = (1 - 2√5 + 5)/(-4)
x = -(6 - 2√5)/(-4)
x = (√5 - 3)/2
