Question

Solve for x: x2 – (1+√5) x + √5 = 0

Answer 1

$Given : x^2 - (1 + \sqrt{5})x + \sqrt{5} = 0$

$= > x^2 - x - \sqrt{5}x + \sqrt{5} = 0$

$= > x^2 - \sqrt{5}x - x + \sqrt{5} = 0$

$= > x(x - \sqrt{5}) - 1(x - \sqrt{5}) = 0$

$= > (x - 1)(x - \sqrt{5}) = 0$

$= > \boxed{x = 1, \sqrt{5}}}$

Hope this helps!

Answer 2

by splitting the middle term we get
x^2- under root 5x - 1x + under root 5 =0
taking common
x (x-root 5 ) - 1 (x-root 5 ) = 0
(x-1)(x-root 5 )=0
so
x-1=0; x=1
also
x-root 5=1
x= root 5
hence we get
x = 1 ; root5